Introduction
microscopic mechanism is regarded as the "jewel in the crown" of condensed matter physics . In the past 30 years, many outstanding research work has emerged, but it is still considered by professionals to be in the stage of blind touching elephants. Today, Mr. Sai recommends popular science articles written by Chen Zhuoyu and Wang Yao, the authors of the journal Science magazine, which have just been published by Mr. Sai at Stanford University, to interpret a new breakthrough in the microscopic mechanism of high temperature superconductivity, and to show the ideas behind the research. This work is regarded as an important improvement in the existing theoretical model. Although it has not yet been able to touch the full image, perhaps this new breakthrough has touched the elephant trunk, which is exciting.
Written by | Chen Zhuoyu (Stanford University)
Wang Yao (Clemson University)
1987, at the March meeting of the American Physics Society, a small conference room was filled with 2,000 physicists and held a report meeting all night. This academic feast shocked the physics community at that time: a type of material called "high temperature superconductors" was discovered.
is different from the previously discovered low-temperature superconductors below 20 K, such as metals and alloys. This type of material only needs to cool to a relatively high temperature (such as the 35 K La-Ba-Cu-O system and 93 K Y-Ba-Cu-O system) [1,2] to achieve electrical conductivity without resistance and at the same time produces a repulsive effect on a very strong magnetic field. With this material, ultra-high resolution medical nuclear magnetic resonance imaging, long-distance lossless power transmission, ultra-high-speed maglev high-speed rail, miniaturized commercial nuclear fusion reactors and other technological applications that change the world are expected to gradually enter people's lives.
high-temperature superconducting material has been discovered for more than 30 years, but the microscopic physical mechanism is still a mystery. In traditional metal alloy superconductors, electrons are paired with each other by the aid of attraction interaction and condense into a superfluid state at low temperatures, so that the current can flow without resistance. The pairing mechanism of high-temperature superconductors is still the jewel of today's condensed matter physics [2]. Understanding the mechanism of high-temperature superconductors can help us design room-temperature superconductors to benefit society.
Recently, the American journal Science published a new achievement of the research on the mechanism of high-temperature superconductivity by Shen Zhixun of Stanford University's research on high-temperature superconductivity "Super Strong Nearest Attraction Force in One-Dimensional Doped Copper Oxygen Chain". The experiment showed evidence of the existence of super nearest neighbor attraction force on the one-dimensional copper oxygen chain, which is of great inspiration for understanding the high-temperature superconductivity pairing mechanism on the two-dimensional copper oxygen surface [3].
Why is the problem of high-temperature superconducting so difficult? Why did the Stanford research team study one-dimensional problems? How will the research team’s discovery help to understand high-temperature superconducting? Below we strive to use simplified popular language to introduce the physics of high-temperature superconducting and the current research progress. You can understand it by having basic physics or chemistry knowledge.
01 Two-dimensional copper oxygen surface
high-temperature superconductors were discovered, scientists soon further discovered that their entire family of copper oxides with similar crystal structures can superconducting [2] at higher temperatures. These compounds all have a two-dimensional copper oxygen surface, which is the channel for superconducting current movement in these materials. In addition to the quasi-two-dimensional copper oxygen surface, it is a charge library for the copper oxygen surface that provides charged load ( carrier ) (see Figure 1) .
Figure 1
Soon physicists learned that the electrons in the copper oxygen surface have strong interactions, which is very different from conventional metal alloy superconductors (in conventional superconductors, the interaction between electrons is very weak, and they can basically be regarded as relatively independent of each other) . The copper oxygen surface is insulated from the beginning, which is very different from ordinary metal materials. This is because there is exactly one electron on each copper atom. Since these electrons are negatively charged, the electrostatic force is mutually repelling and can only occupy their own position and cannot move.It's like traffic jams on the road, with too many cars crowded and no one can move.
is the help of the charge library layer so that the copper oxygen surface can conduct electricity, or even superconducting. This charge library can snatch electrons from the copper oxygen surface, just like removing some cars on a traffic jam, and the road can be smooth. Specifically, the entire solid material is electrically neutral. In addition to electrons, there are metal cations with positive charge (such as copper ion ) , forming a positive charge background. Originally, every position was filled with electrons. If an electron was taken out, a positively charged hole appeared. Because there was a space, the electron could move. For example, a negatively charged electron moves to the right, which is actually equivalent to a positively charged hole moving to the left. In this case, instead of considering a large number of electrons, it is better to regard the hole as a positively charged particle, equivalent to the antiparticle of the electron, which is more physically intuitive.
So how to add more holes to a copper oxide? Material physicists achieve this through "doping", which is to dopate "impurity" atoms into the charge bank. If the impurity atom has fewer electrons than the original atom, it will snatch electrons from the copper oxygen surface, so that the number of holes in the copper oxygen surface becomes more and can conduct electricity, and even superconducting appears at a sufficiently low temperature.
In-depth reading:
In the undoped intrinsic state of the copper oxygen surface, 9 electrons are filled with each divalent copper ion, of which 1 electron is on the 3dx2-y2 orbit with the highest energy, while 10 electrons are required to completely fill the 3d orbit. In the energy band theory, this unfilled energy band is electrically conductive. However, modern quantum chemistry has revealed that d-orbital electrons have a strong correlation effect: the electrons on the 3dx2-y2 orbital of copper atoms are mutually repulsive by electrostatic repulsion, and each electron can only occupy its own position and cannot move.
Therefore, the undoped copper oxide is the so-called Mott insulator, not the conductor with the predicted band theory. Another theory that may be more precise is the charge transfer insulator, because there is a strong hybridization between the copper orbit and the oxygen orbit near the Fermi surface. The so-called charge transfer refers to the charge transfer between copper and oxygen. When doping generates holes, the holes can flow as positively charged carriers in the copper oxygen surface. There are many methods for doping
. In addition to replacing positive ion , the vacancies in lattice can also be replaced with oxygen in oxide . The vacant position does not contain electrons, but the oxygen atom can be understood as carrying -2 electrons, and doping oxygen into the oxide means doping holes into it. On the contrary, if oxygen is taken away from the oxide and the oxygen vacant is left, it is to add electrons to it.
02 Hubbard model
To understand the mechanism of high temperature superconductivity, we can start with the Hubbard model. The study of the strong correlation Hubbard model in the physics community began before the discovery of high-temperature superconducting. Like many branches in physics, at first this model was just a toy for theorists. However, the discovery of high-temperature superconducting has pushed this model to the forefront of physics. A group of physicists represented by Professor P. W. Anderson, Professor T. M. Rice and Professor Zhang Fuchun established the core position of the Hubbard model in understanding the mechanism of high temperature superconductivity [4-6].
When we were learning atoms in junior high school, the first thing we learned was the hydrogen atom model, because hydrogen atom only has one proton and one electron, which is the simplest, but the hydrogen atom model basically contains a considerable amount of content in atomic physics. It can be said that after understanding the hydrogen atom model, the rest of atomic physics basically just repair this model. The Hubbard (Hubbard) model is the existence of a hydrogen atom model in a strongly associated electronic system. It is very simple, but it explains a lot of complex phenomena in a strongly associated electronic system.High-temperature superconductors are the most representative highly correlated electronic systems, because the interaction between electrons is very strong. As mentioned in the previous section, electrons will squeeze each other and cannot move due to strong repulsion.
The main two parameters U and t in the Hubbard model are very intuitive in physical meaning. If two electrons occupy the same position, due to electrostatic repulsion, the increased energy of the system is U, which is equivalent to potential energy. An electron wants to jump from one position to an adjacent position, and the energy falling by the system is t, which is equivalent to kinetic energy.
Hubbard's model is simple, but it can explain a large number of experimental phenomena [7-14]. For example, as mentioned above, since two electrons are stacked in the same position, it takes a lot of energy (U is much greater than t) , so when each position in the copper oxygen surface occupies an electron, the copper oxygen surface is an insulator. Once the copper oxygen surface is doped with enough holes, the electrons can move and can conduct electricity. The Hubbard model also successfully explained a series of more complex strong correlations such as antiferromagnetic sequence, such as quantum states, . In the next section, we will further introduce how it predicts one-dimensional antiferromagnetic.
Although the Hubbard model is successful in all aspects, many different methods have found signs of superconducting state in approximate solutions or precise solutions of quasi-one-dimensional systems [15-23]. However, the precise solution to the high-temperature superconducting phenomenon cannot be given yet. The main problem is that the copper oxygen surface is a quasi-two-dimensional system. Faced with a large number of strongly correlated electrons, a simple two-dimensional Hubbard model is powerless. This is a bit similar to the well-known three-body problem. Although the Newton 0,000 law of gravity is simple, as long as there are three celestial bodies interacting, it will be very difficult to get an accurate solution. In actual material systems, the number of electrons is an extremely terrifying order of 10 to the power of 23. This arduous task is still beyond the reach of human computing power.
Since the two-dimensional Hubbard model cannot obtain an accurate solution, when comparing it with experiments, it is impossible to give a deterministic conclusion within the framework of scientific methodology: If the theoretical predictions do not match the experiment, we cannot know whether it is the error caused by the calculation process, or whether the Hubbard model itself is not enough to explain the phenomenon.
However, for one-dimensional systems, since the dimension is missing one dimension, the complexity of the solution is greatly reduced. With the help of supercomputers, there is a way to get an accurate solution in one-dimensional [24-26]! If we can find a one-dimensional material system corresponding to two-dimensional, experiments and theories can accurately compare them, and we can know whether the theoretical model is right!
Therefore, studying one-dimensional systems has become the key to understanding the microscopic model of high-temperature superconducting of copper oxides.
In-depth reading:
After the discovery of high-temperature superconducting, P.W. Anderson pointed out that high-temperature superconducting in copper oxides may originate from the RVB state in Hubbard's model [4]. Then, a group of physicists represented by Zhang Fuchun , based on the orbital interaction of specific copper oxides, explained the correspondence between its low-energy effective model and the Hubbard model [5,6]. Although the parameters in strong correlation models are difficult to determine through numerical calculations, long-term theoretical and experimental comparisons have basically determined the range of these two parameters in Hubbard's model.
In addition to Motel insulators and antiferromagnets, the Hubbard model also successfully predicted more complex electron collective behaviors such as stripes, strange metals, charge density waves, etc. in strongly correlated electronic systems. It can be said to be the most successful and concise model in strongly associated electronic systems [7-14].
More specifically, the two-dimensional Hubbard model cannot obtain an exact solution because of the quantum entanglement effect caused by strong correlation, which causes the effective degree of freedom of the system to increase exponentially with the increase of the scale, while classical computers can only simulate one part.Moreover, the two-dimensional Hubbard model gives a series of quantum states with similar energy and incompatible energy. Even today's most advanced numerical simulation methods (such as quantum Monte Carlo and tensor networks) cannot accurately predict what will happen. Its precise solutions may depend on future quantum computing or quantum simulations to reveal [27-31].
03 One-dimensional copper oxygen chain: spin charge separation
Many physics have completely changed when the dimensions are different. The Hubbard model exhibits very strange properties in one dimension. To understand the one-dimensional strong correlation electronic system, we also need to understand the concept of spin (spin) and the principle of Pauli incompatibility in .
As elementary particles, electrons have three intrinsic physical properties: mass, charge, and spin . How to understand spin? The spin can be compared to a small magnet, and each electron itself can be regarded as a small magnetic needle. small magnetic needle has a pointing point, such as upward or downward, as shown in Figure 2.
Figure 2
In the process of establishing quantum mechanics , Pauli is an important physicist. The Pauli incompatibility principle is a basic principle in quantum mechanics, which is equivalent to the position of Newton's law in classical mechanics.
incompatibility principle says that two electrons cannot be in exactly the same state. For example, in the Hubbard model, if two electrons want to occupy the same position, their spins cannot be the same, and they must be opposite.
If there is an electron at each position on a one-dimensional copper oxygen chain, the adjacent electrons will also be close to each other and do not like the electrons next to them as they are. As a result, the adjacent electrons are spinning opposite, forming an order with interlaced spin directions, which is physically called antiferromagnetic order, as shown in Figure 3.
Figure 3
Magic things are coming. If we remove an electron from this antiferromagnetic electronic link, for example, use light to create an electron, as shown in Figure 4, when the electrons in the electronic link move and interact with each other (see the figure for details) , charge and spin, as the two basic properties of electrons, actually move independently.
The vacancies that move only carry the property of charge. Physicists call it vacancies (holon, not called "holes" but renamed "vacancies" to emphasize that it only has charge but no spins) . The state of adjacent spins in the same direction has the properties of spin, which physicists call spin sub (spinon). This phenomenon of spin charge separation in one-dimensional electron chain is completely different from the properties of electrons in free space. This is the most prominent manifestation of collective behavior different from individual behavior.
Figure 4
The above are all prophecies based on the simplest Hubbard model, but the real materials are not as simple as toy models after all. Then whether this prediction is correct depends on experiments. The predecessors have synthesized undoped copper oxygen chain parent material, and have verified the phenomenon of spin charge separation in one-dimensional copper oxygen chains through a series of experiments, which indirectly confirms the reliability of the Hubbard model in the copper oxide material system [32-35].
However, the previous experiments were done in undoped copper oxygen chains, which means that each time, one loophole and one spinn were tapped with light. Although the spin charge separation was seen, the interaction between the two charge carriers (that is, the loophole) could not be seen. We mentioned earlier that the difficult and key points in the research on high-temperature superconducting mechanism are the pairing of carriers and the interaction between carriers, which are the core issues we are concerned about.
In fact, experimental physicists have been working hard for more than 20 years in order to make doped copper oxygen chains. It was not until today that the research team solved this problem and achieved a very wide range of controllable doping and spectral characterization up to 40%, unveiling the mystery of the interaction between two carriers in copper oxides.
Cute women cannot cook without rice. The key to this success is a newly built cutting-edge equipment: a combined system of oxide molecular beam epitaxial and synchronous radiation angle resolution photoelectron spectrometer. Using this set of equipment, the newly prepared film can be kept in an ultra-high vacuum from the preparation chamber to the measurement chamber of the photoelectron spectrometer, and then detect the energy momentum junction distribution of electrons within the system, directly obtaining the most core physical properties of quantum material , avoiding the problem that some special phases cannot exist stably in the air. This top-notch joint system is located in the SLAC National Laboratory, right next to Stanford University.
Now this set of cutting-edge equipment is a powerful tool for studying the quasi-one-dimensional copper oxygen chain material system. The low-dimensional geometric structure of this material causes it to be very unstable. For bulk materials, only the undoped parent can exist more stably. Therefore, previous research on doping the next-dimensional copper oxygen chain has remained at the theoretical level [24-26]. But the films in this ultra-vacuum environment are different. Baking this film containing one-dimensional copper oxygen chains with ozone can change the density of carriers in the copper oxygen chain and can perform spectral measurements at the same time. Based on this idea, the research team conducted a systematic measurement of the material in order to obtain the information on doping of the one-dimensional system corresponding to the quasi-two-dimensional copper oxide superconductor [3].
In-depth reading:
The movement of the airborne is mainly determined by t, while the movement of the spin sub is mainly determined by the energy of spin interaction J=4t2/U, so the movement speed of the airborne and spin sub is not the same. In the angle-resolved photoelectron spectrum (ARPES), two non-coinciding branches will be seen. However, in undoped systems, no information related to the interaction between carriers is seen in ARPES. The key to achieving controllable doping of copper oxygen chains in the experiment is the combination of film growth and ozone baking, which can controllable the oxygen content in the crystal lattice, and oxygen atoms provide holes to the system [36].
oxide film growth and synchronous radiation ARPES ultra-high vacuum interconnection is the key to the success of the experiment, and there are three reasons: (1) This compound is extremely sensitive to air and decomposes within a few seconds when it touches air; (2) ARPES measurement requires extremely high surface quality, and the deposits in the air will have a fatal impact on the spectral mass; (3) The photon energy required for measurement can be provided by synchronous radiation.
04 First discovery: Super nearest neighbor attraction
uses large scientific equipment to synchronize the light source. In the world's most advanced angle resolution photoelectron spectrometer, we can see the loophole (holon) and the interaction between the loopholes [3]. Specifically, there is a peak in the momentum distribution curve of the photoelectron spectrum, representing the intensity of the interaction between this hollows [37,38]. The red line shown in Figure 5 is an experimental curve measured in the one-dimensional copper oxygen chain. The two in the middle are the main peaks representing the loopholes, and there are obviously a pair of strong "shoulders" on both sides. This "shoulder" is the characteristic peak of the interaction between the loopholes.
Figure 5
In a one-dimensional system, computer theoretical numerical simulation can give accurate predictions of different theoretical models. We see that in the prediction curve given by the pure Hubbard model, the shoulder characteristics are particularly weak and almost invisible, which obviously cannot match the experiment. If the Hubbard model is based on the Nearest Repulsion (simulating the long-range electrostatic Coulomb interaction between electrons) , even if the repulsion is very strong, the strength of the shoulder cannot be strengthened.But on the contrary, if you are based on the Hubbard model and the strong attraction of the neighbors, it will be very consistent with the experimental curve!
The nearest neighbor has a very strong attraction. Based on the mathematical form of spin charge separation in Hubbard's model itself, we can actually derive the effective attraction between a loophole. However, the attraction found in the experiment is ten times the intensity of the nearest neighbors included in the Hubbard model! Not only that, this experiment also systematically measured copper oxygen chains of different doping degrees, and the theoretical prediction of strong attraction of nearest neighbors of the same intensity was very well matched with all experimental spectral lines!
This shows that in real copper oxide, there is a strong near-neighbor attraction, and the source of this attraction is outside the Hubbard model. Since the structure of quasi-one-dimensional copper oxygen chain and quasi-two-dimensional copper oxygen surface is very similar, the one-dimensional quantum microscopic theoretical model can be generalized to 2D after certain corrections. The "Hubbard + Nearest Neighbor Attraction" model in the paper is based on the great success of the Hubbard model itself. Coupled with the newly discovered evidence of super nearest neighbor attraction, it helps with high-temperature superconducting electron pairing. We believe that this may be a complete theoretical model describing high-temperature superconductors!
In-depth reading:
ARPES can measure the kinetic energy and momentum of photoelectrons at the same time. Due to the energy conservation law of momentum inversely elicits the energy and momentum information of electrons in materials. Figure 5 shows the momentum distribution curve of binding energy below a certain Fermi surface. In one-dimensional strongly correlated electronic systems, the behavior of electrons affects each other and physically reflects more collective characteristics than individual characteristics. Therefore, the spectral lines of ARPES will usually become wider than those of higher dimensions.
theoretical numerical simulation can accurately calculate the spectral function of a one-dimensional system and compare it with ARPES data one by one, so a more accurate conclusion can be drawn. The attraction of this neighbor can be expressed as V~-t, which is ten times greater than the effective attraction intensity V~-0.1t generated by the Hubbard model itself through low energy projection.
05 Possible sources of super nearest neighbor attraction: Phonon
So what is the source of attraction between this electron and electron (or holes and holes) ? There should not be a mutually attractive electrostatic force between the positively charged holes.
People often say that they don’t know the true face of Mount Lu because they are in this mountain. If we only consider the electrons in solids, of course it is impossible to attract each other. But don't forget that the whole solid is electrically neutral, in addition to electrons, there are also positively charged metal cation (here "yang" means positively charged) The positively charged background formed by the lattice. Since the cations also move slightly, the electrons are actually moving in a positively charged grid that can vibrate!
Solid Physics , we mathematically describe the weak vibration of cations as a kind of quasi-particle : when there is no vibration, it means that this quasi-particle is not produced, and an increase in the amplitude means that the number of such particles increases. This quasi-particle is called phonon . When we consider the attraction between phonon (lattice vibration) and electrons, we will find that phonons can serve as a medium to generate attraction between electrons!
Imagine that you throw glass balls on a flat plate, and these glass balls will be scattered everywhere due to the collision between balls, which is similar to the case of pure electronic systems. But if we throw glass balls on the soft mattress, you will find those balls gather together. This is because when one ball presses the mattress out of a pit, the second ball will tend to fall into the pit to reduce potential energy. If we only care about the position of the balls and ignore the background of the mattress, it looks like these glass balls are attractive to each other.
Similarly, the vibration of the lattice composed of cations in a solid will induce an attraction between electrons like a mattress.This interaction between lattice vibration and electrons, we call electrophonon coupling, is actually the mechanism of conventional metal superconducting! Badin , Cooper and Schrief won the 1972 Nobel Prize in Physics [39] for creating this theory (named "BCS Theory" after them) .
Using this phonon as the media attraction mechanism, can we explain the nearest neighbor attraction found in the copper oxygen chain? It can be proved in theory that when the frequency of phonon (that is, lattice vibration) is very high, this interaction only exists between different electrons of in the same unit cell (the so-called unit cell is a unit of the lattice, and the unit cell periodically is the lattice) ; but when the frequency gradually decreases, this interaction can extend to a longer distance.
also uses glass balls and mattresses as an example: imagine that glass balls are constantly moving on the mattress. If the recovery speed of the mattress is very fast, then after a glass ball rolls over, the deformation of the mattress will immediately recover, and the glass balls moving from a distance will not feel the pit left by the former; only when the recovery speed of the mattress is much smaller than the movement speed of the glass balls, this pit potential energy can be transmitted to other glass balls farther away. Based on this principle, we quantitatively analyze the known electrophonon coupled intensity and possible near-neighbor attraction interactions. Unfortunately, this value is much smaller than the intensity of the attractiveness we need. Is
a problem with the theoretical model, or is there a more complex degree of freedom at work? This problem has troubled physicists for a long time. After re-examining the entire logical framework, we may be influenced by the ideas of conventional superconducting BCS theory. It is generally believed that the coupling of electrophonons must be the strongest when the distance is closest, and rapidly decays with distance. Therefore, generally speaking, only coupling at the same unit cell position is considered and other farther situations are ignored. The physical properties of conventional superconducting materials estimated from this are also basically consistent with the experimental results.
However, for copper oxides, since the Hubbard model has revealed that there is extremely strong repulsion at the same unit cell position, what should be more concerned about is the electron interaction between two adjacent unit cell positions. Naturally, the main contribution of this near-neighbor unit cell interaction should not come from the electrophonon coupling within the unit cell, but the electrophonon coupling between the unit cells. Based on this idea, supplemented by the latest developed non-Gaussian state precision diagonalization method [40], the research team analyzed the impact of long-range electrophonon coupling on this effective attraction. As expected, its contribution is much greater than the aforementioned estimate that only considers the electrophonon coupling in the unit cell. Moreover, the intensity of this effective attraction is very consistent with the experimental results [41].
Of course, the above discussion on the source of attractiveness of this nearest neighbor is only a theoretical explanation and prediction. A more stringent conclusion still requires further experimental analysis of in different copper oxides (especially in high-temperature superconducting materials). It is worth emphasizing that if the above mechanism is ultimately proven to be correct, electrophonon coupling will become the last step in solving the problem of high-temperature superconducting, but its mechanism of action is completely different from that of traditional BCS superconducting, and the apparent phenomena generated are also very different.
In high-temperature superconducting materials, the strong correlation effect between electrons is still the most significant phenomenon. Therefore, it is the mutual cooperation and competition between strong electron correlation and electrophonon coupling that creates this strange physical phenomenon. Because these two interactions are widely present in materials, it may contain richer physics and more valuable applications. The theoretical models, numerical technologies that have flourished in recent years, as well as the constantly improved experimental methods and characterization accuracy, are expected to rapidly advance research in this direction.
In-depth reading:
Phonons can be quadratic quantized to describe more microscopic, quantized vibration patterns. This mechanism of mutual attraction was actually proposed and verified in the middle of the last century.When this attraction is strong enough, electrons tend to exist and move in pairs, forming a new bound state: Cooper pair. This pair of electrons presents the properties of bosons and therefore are not scattered in motion, reflecting superconductivity. This theory is one of the most famous discoveries in solid physics: BCS theory. It successfully explains the superconducting phenomenon of most substances at low temperatures. Later, after various improvements to different degrees, the description of the superconducting phenomenon was improved from qualitative to quantitative magnitude [42-45]. The electron pairing mechanism in
copper oxygen superconductor is different from that of traditional BCS superconductors, and the phenomena produced are also different. For example, Cooper pairs in copper oxygen superconductors show d-wave symmetry, rather than s-wave symmetry. The parent body of the superconductor is an antiferromagnetic insulator. Through the non-Gaussian precise diagonalization method, if we bring in the known electrophonon coupling intensity and phonon frequency, and consider the coupling effect naturally attenuates with distance according to the law of electromagnetic force, the long-range electrophonon coupling gives the intensity of this effective attraction interaction, which is exactly V=-t, which is completely consistent with the experimental results.
06 Outlook: How to design a higher temperature high-temperature superconductor
So far, through experimental and theoretical comparisons, we not only found an important evidence of an important ultra-strong nearest electron attraction interaction that has been ignored before, but also quantitatively explained at the microscopic level that this interaction may originate from phonons. Although phonons seem to play an important role in both conventional superconductors and copper oxide superconductors, it does not mean that we are back to the simple explanation of the superconducting of electrophonon coupling.
We have actually reached a deeper understanding of high-temperature superconducting pairing, the most profound quantum mechanics problem in today's era: electron-electron interaction and electron-phonon interaction work together to create these wonderful physical phenomena in strongly related electronic systems. Of course, it may be necessary to complete this story more direct experimental evidence and theoretical calculation efforts, but we may be about to reach the ending. Behind this seemingly simple story, it actually contains a large number of innovations in experimental techniques and theoretical numerical methods from the scientific community. Scientific discoveries often do not rely on inspirational ideas, but are more about the improvement and iteration of instruments, materials, algorithms, and models.
high-temperature superconducting mechanism is a topic that is no longer young. In the process of two to three generations of people continuously charging them, the exploration of the final mechanism is of the top priority, but the technological innovations generated in this process cannot be ignored.
For example, in terms of experiments, a variety of characterization technologies represented by angle resolution photoelectron spectrometer (ARPES) have made great progress in the research of high-temperature superconducting, and later shines in the research of topological materials. In terms of theory, computational physics methods represented by density matrix reforming groups closely combine physical theory with modern scientific computing technology, greatly deepening our understanding of cutting-edge problems such as quantum entanglement. Of course, other slight improvements and even failed attempts in experiments, theory, numerical aspects are solidifying our inspiring ideas into knowledge that has been tempered.
Understanding the mechanism of high-temperature superconductors is not only of great scientific significance, but also hopes to design high-temperature superconductors with higher transition temperatures based on these scientific understandings, and finally be implemented experimentally. If the materials at room temperature (that is, 300K, equivalent to 27℃) and normal pressure (that is, a standard atmospheric pressure) can be superconductive and conductivity can be without resistance, and the entire human society based on the electrical industry will undergo tremendous changes.
Based on the current understanding of the mechanism of high-temperature superconductor, can higher-temperature superconductors be designed? The answer is: We are already on the way!
We have realized that the Hubbard model provides a platform for basic electronic systems, and the key to high-temperature superconducting pairing may be due to the strong near-neighbor attraction brought by phonons. In this way, if we want to obtain stronger near-neighbor attraction, we need to further optimize the phonon mode and the electron phonon coupling strength.
A possible solution is to combine the two-dimensional copper oxygen surface with a charge bank with a better phonon frequency through a heterojunction, which in principle should further increase the superconducting transition temperature. In terms of specific implementation, there is still a lot of work to be done in material engineering for copper oxide high-temperature superconductors, but for another type of high-temperature superconductor - iron-based superconductors, there have been some delightful attempts [47-49].
Even based on existing copper-based high-temperature superconducting materials, the industrial application of high-temperature superconducting has gradually entered a good state. It has broad development prospects in the fields of strategic technology (such as high-temperature superconducting controlled nuclear fusion and the new generation of high-energy particle accelerator), , transportation (such as high-temperature superconducting magnetic levitation trains and ship motors), , medical (such as ultra-high resolution nuclear magnetic resonance imaging and quantum interference cardioencephalography), , electric power (such as high-temperature superconducting energy storage devices, cables, fault current limiters, transformers, generators), , communication (such as high-temperature superconducting microwave filters, oscillators, single-photon detectors and terahertz detectors) and other fields.
Introduction microscopic mechanism is regarded as the "jewel in the crown" of condensed matter physics . In the past 30 years, many outstanding research work has emerged, but it is still considered by professionals to be in the stage of blind touching elephants. Today, Mr. Sai recommends popular science articles written by Chen Zhuoyu and Wang Yao, the authors of the journal Science magazine, which have just been published by Mr. Sai at Stanford University, to interpret a new breakthrough in the microscopic mechanism of high temperature superconductivity, and to show the ideas behind the research. This work is regarded as an important improvement in the existing theoretical model. Although it has not yet been able to touch the full image, perhaps this new breakthrough has touched the elephant trunk, which is exciting. Written by | Chen Zhuoyu (Stanford University) Wang Yao (Clemson University) 1987, at the March meeting of the American Physics Society, a small conference room was filled with 2,000 physicists and held a report meeting all night. This academic feast shocked the physics community at that time: a type of material called "high temperature superconductors" was discovered. is different from the previously discovered low-temperature superconductors below 20 K, such as metals and alloys. This type of material only needs to cool to a relatively high temperature (such as the 35 K La-Ba-Cu-O system and 93 K Y-Ba-Cu-O system) [1,2] to achieve electrical conductivity without resistance and at the same time produces a repulsive effect on a very strong magnetic field. With this material, ultra-high resolution medical nuclear magnetic resonance imaging, long-distance lossless power transmission, ultra-high-speed maglev high-speed rail, miniaturized commercial nuclear fusion reactors and other technological applications that change the world are expected to gradually enter people's lives. high-temperature superconducting material has been discovered for more than 30 years, but the microscopic physical mechanism is still a mystery. In traditional metal alloy superconductors, electrons are paired with each other by the aid of attraction interaction and condense into a superfluid state at low temperatures, so that the current can flow without resistance. The pairing mechanism of high-temperature superconductors is still the jewel of today's condensed matter physics [2]. Understanding the mechanism of high-temperature superconductors can help us design room-temperature superconductors to benefit society. Recently, the American journal Science published a new achievement of the research on the mechanism of high-temperature superconductivity by Shen Zhixun of Stanford University's research on high-temperature superconductivity "Super Strong Nearest Attraction Force in One-Dimensional Doped Copper Oxygen Chain". The experiment showed evidence of the existence of super nearest neighbor attraction force on the one-dimensional copper oxygen chain, which is of great inspiration for understanding the high-temperature superconductivity pairing mechanism on the two-dimensional copper oxygen surface [3]. Why is the problem of high-temperature superconducting so difficult? Why did the Stanford research team study one-dimensional problems? How will the research team’s discovery help to understand high-temperature superconducting? Below we strive to use simplified popular language to introduce the physics of high-temperature superconducting and the current research progress. You can understand it by having basic physics or chemistry knowledge. high-temperature superconductors were discovered, scientists soon further discovered that their entire family of copper oxides with similar crystal structures can superconducting [2] at higher temperatures. These compounds all have a two-dimensional copper oxygen surface, which is the channel for superconducting current movement in these materials. In addition to the quasi-two-dimensional copper oxygen surface, it is a charge library for the copper oxygen surface that provides charged load ( carrier ) (see Figure 1) .
In short, it has been 34 years since the research on high-temperature superconductivity. Although there are still many unsolved mysteries, humans have become more and more deeply aware of it. Therefore, they have also made more extensive developments in important disciplines such as quantum multibody physics, quantum materials, quantum chemistry, etc. step by step. The mechanism of high-temperature superconducting is still the jewel in the crown of condensed matter physics, but the moment humans really take it off should not be too far away.01 Two-dimensional copper oxygen surface
Figure 1
Soon physicists learned that the electrons in the copper oxygen surface have strong interactions, which is very different from conventional metal alloy superconductors (in conventional superconductors, the interaction between electrons is very weak, and they can basically be regarded as relatively independent of each other) . The copper oxygen surface is insulated from the beginning, which is very different from ordinary metal materials. This is because there is exactly one electron on each copper atom. Since these electrons are negatively charged, the electrostatic force is mutually repelling and can only occupy their own position and cannot move.It's like traffic jams on the road, with too many cars crowded and no one can move.
is the help of the charge library layer so that the copper oxygen surface can conduct electricity, or even superconducting. This charge library can snatch electrons from the copper oxygen surface, just like removing some cars on a traffic jam, and the road can be smooth. Specifically, the entire solid material is electrically neutral. In addition to electrons, there are metal cations with positive charge (such as copper ion ) , forming a positive charge background. Originally, every position was filled with electrons. If an electron was taken out, a positively charged hole appeared. Because there was a space, the electron could move. For example, a negatively charged electron moves to the right, which is actually equivalent to a positively charged hole moving to the left. In this case, instead of considering a large number of electrons, it is better to regard the hole as a positively charged particle, equivalent to the antiparticle of the electron, which is more physically intuitive.
So how to add more holes to a copper oxide? Material physicists achieve this through "doping", which is to dopate "impurity" atoms into the charge bank. If the impurity atom has fewer electrons than the original atom, it will snatch electrons from the copper oxygen surface, so that the number of holes in the copper oxygen surface becomes more and can conduct electricity, and even superconducting appears at a sufficiently low temperature.
In-depth reading:
In the undoped intrinsic state of the copper oxygen surface, 9 electrons are filled with each divalent copper ion, of which 1 electron is on the 3dx2-y2 orbit with the highest energy, while 10 electrons are required to completely fill the 3d orbit. In the energy band theory, this unfilled energy band is electrically conductive. However, modern quantum chemistry has revealed that d-orbital electrons have a strong correlation effect: the electrons on the 3dx2-y2 orbital of copper atoms are mutually repulsive by electrostatic repulsion, and each electron can only occupy its own position and cannot move.
Therefore, the undoped copper oxide is the so-called Mott insulator, not the conductor with the predicted band theory. Another theory that may be more precise is the charge transfer insulator, because there is a strong hybridization between the copper orbit and the oxygen orbit near the Fermi surface. The so-called charge transfer refers to the charge transfer between copper and oxygen. When doping generates holes, the holes can flow as positively charged carriers in the copper oxygen surface. There are many methods for doping
. In addition to replacing positive ion , the vacancies in lattice can also be replaced with oxygen in oxide . The vacant position does not contain electrons, but the oxygen atom can be understood as carrying -2 electrons, and doping oxygen into the oxide means doping holes into it. On the contrary, if oxygen is taken away from the oxide and the oxygen vacant is left, it is to add electrons to it.
02 Hubbard model
To understand the mechanism of high temperature superconductivity, we can start with the Hubbard model. The study of the strong correlation Hubbard model in the physics community began before the discovery of high-temperature superconducting. Like many branches in physics, at first this model was just a toy for theorists. However, the discovery of high-temperature superconducting has pushed this model to the forefront of physics. A group of physicists represented by Professor P. W. Anderson, Professor T. M. Rice and Professor Zhang Fuchun established the core position of the Hubbard model in understanding the mechanism of high temperature superconductivity [4-6].
When we were learning atoms in junior high school, the first thing we learned was the hydrogen atom model, because hydrogen atom only has one proton and one electron, which is the simplest, but the hydrogen atom model basically contains a considerable amount of content in atomic physics. It can be said that after understanding the hydrogen atom model, the rest of atomic physics basically just repair this model. The Hubbard (Hubbard) model is the existence of a hydrogen atom model in a strongly associated electronic system. It is very simple, but it explains a lot of complex phenomena in a strongly associated electronic system.High-temperature superconductors are the most representative highly correlated electronic systems, because the interaction between electrons is very strong. As mentioned in the previous section, electrons will squeeze each other and cannot move due to strong repulsion.
The main two parameters U and t in the Hubbard model are very intuitive in physical meaning. If two electrons occupy the same position, due to electrostatic repulsion, the increased energy of the system is U, which is equivalent to potential energy. An electron wants to jump from one position to an adjacent position, and the energy falling by the system is t, which is equivalent to kinetic energy.
Hubbard's model is simple, but it can explain a large number of experimental phenomena [7-14]. For example, as mentioned above, since two electrons are stacked in the same position, it takes a lot of energy (U is much greater than t) , so when each position in the copper oxygen surface occupies an electron, the copper oxygen surface is an insulator. Once the copper oxygen surface is doped with enough holes, the electrons can move and can conduct electricity. The Hubbard model also successfully explained a series of more complex strong correlations such as antiferromagnetic sequence, such as quantum states, . In the next section, we will further introduce how it predicts one-dimensional antiferromagnetic.
Although the Hubbard model is successful in all aspects, many different methods have found signs of superconducting state in approximate solutions or precise solutions of quasi-one-dimensional systems [15-23]. However, the precise solution to the high-temperature superconducting phenomenon cannot be given yet. The main problem is that the copper oxygen surface is a quasi-two-dimensional system. Faced with a large number of strongly correlated electrons, a simple two-dimensional Hubbard model is powerless. This is a bit similar to the well-known three-body problem. Although the Newton 0,000 law of gravity is simple, as long as there are three celestial bodies interacting, it will be very difficult to get an accurate solution. In actual material systems, the number of electrons is an extremely terrifying order of 10 to the power of 23. This arduous task is still beyond the reach of human computing power.
Since the two-dimensional Hubbard model cannot obtain an accurate solution, when comparing it with experiments, it is impossible to give a deterministic conclusion within the framework of scientific methodology: If the theoretical predictions do not match the experiment, we cannot know whether it is the error caused by the calculation process, or whether the Hubbard model itself is not enough to explain the phenomenon.
However, for one-dimensional systems, since the dimension is missing one dimension, the complexity of the solution is greatly reduced. With the help of supercomputers, there is a way to get an accurate solution in one-dimensional [24-26]! If we can find a one-dimensional material system corresponding to two-dimensional, experiments and theories can accurately compare them, and we can know whether the theoretical model is right!
Therefore, studying one-dimensional systems has become the key to understanding the microscopic model of high-temperature superconducting of copper oxides.
In-depth reading:
After the discovery of high-temperature superconducting, P.W. Anderson pointed out that high-temperature superconducting in copper oxides may originate from the RVB state in Hubbard's model [4]. Then, a group of physicists represented by Zhang Fuchun , based on the orbital interaction of specific copper oxides, explained the correspondence between its low-energy effective model and the Hubbard model [5,6]. Although the parameters in strong correlation models are difficult to determine through numerical calculations, long-term theoretical and experimental comparisons have basically determined the range of these two parameters in Hubbard's model.
In addition to Motel insulators and antiferromagnets, the Hubbard model also successfully predicted more complex electron collective behaviors such as stripes, strange metals, charge density waves, etc. in strongly correlated electronic systems. It can be said to be the most successful and concise model in strongly associated electronic systems [7-14].
More specifically, the two-dimensional Hubbard model cannot obtain an exact solution because of the quantum entanglement effect caused by strong correlation, which causes the effective degree of freedom of the system to increase exponentially with the increase of the scale, while classical computers can only simulate one part.Moreover, the two-dimensional Hubbard model gives a series of quantum states with similar energy and incompatible energy. Even today's most advanced numerical simulation methods (such as quantum Monte Carlo and tensor networks) cannot accurately predict what will happen. Its precise solutions may depend on future quantum computing or quantum simulations to reveal [27-31].
03 One-dimensional copper oxygen chain: spin charge separation
Many physics have completely changed when the dimensions are different. The Hubbard model exhibits very strange properties in one dimension. To understand the one-dimensional strong correlation electronic system, we also need to understand the concept of spin (spin) and the principle of Pauli incompatibility in .
As elementary particles, electrons have three intrinsic physical properties: mass, charge, and spin . How to understand spin? The spin can be compared to a small magnet, and each electron itself can be regarded as a small magnetic needle. small magnetic needle has a pointing point, such as upward or downward, as shown in Figure 2.
Figure 2
In the process of establishing quantum mechanics , Pauli is an important physicist. The Pauli incompatibility principle is a basic principle in quantum mechanics, which is equivalent to the position of Newton's law in classical mechanics.
incompatibility principle says that two electrons cannot be in exactly the same state. For example, in the Hubbard model, if two electrons want to occupy the same position, their spins cannot be the same, and they must be opposite.
If there is an electron at each position on a one-dimensional copper oxygen chain, the adjacent electrons will also be close to each other and do not like the electrons next to them as they are. As a result, the adjacent electrons are spinning opposite, forming an order with interlaced spin directions, which is physically called antiferromagnetic order, as shown in Figure 3.
Figure 3
Magic things are coming. If we remove an electron from this antiferromagnetic electronic link, for example, use light to create an electron, as shown in Figure 4, when the electrons in the electronic link move and interact with each other (see the figure for details) , charge and spin, as the two basic properties of electrons, actually move independently.
The vacancies that move only carry the property of charge. Physicists call it vacancies (holon, not called "holes" but renamed "vacancies" to emphasize that it only has charge but no spins) . The state of adjacent spins in the same direction has the properties of spin, which physicists call spin sub (spinon). This phenomenon of spin charge separation in one-dimensional electron chain is completely different from the properties of electrons in free space. This is the most prominent manifestation of collective behavior different from individual behavior.
Figure 4
The above are all prophecies based on the simplest Hubbard model, but the real materials are not as simple as toy models after all. Then whether this prediction is correct depends on experiments. The predecessors have synthesized undoped copper oxygen chain parent material, and have verified the phenomenon of spin charge separation in one-dimensional copper oxygen chains through a series of experiments, which indirectly confirms the reliability of the Hubbard model in the copper oxide material system [32-35].
However, the previous experiments were done in undoped copper oxygen chains, which means that each time, one loophole and one spinn were tapped with light. Although the spin charge separation was seen, the interaction between the two charge carriers (that is, the loophole) could not be seen. We mentioned earlier that the difficult and key points in the research on high-temperature superconducting mechanism are the pairing of carriers and the interaction between carriers, which are the core issues we are concerned about.
In fact, experimental physicists have been working hard for more than 20 years in order to make doped copper oxygen chains. It was not until today that the research team solved this problem and achieved a very wide range of controllable doping and spectral characterization up to 40%, unveiling the mystery of the interaction between two carriers in copper oxides.
Cute women cannot cook without rice. The key to this success is a newly built cutting-edge equipment: a combined system of oxide molecular beam epitaxial and synchronous radiation angle resolution photoelectron spectrometer. Using this set of equipment, the newly prepared film can be kept in an ultra-high vacuum from the preparation chamber to the measurement chamber of the photoelectron spectrometer, and then detect the energy momentum junction distribution of electrons within the system, directly obtaining the most core physical properties of quantum material , avoiding the problem that some special phases cannot exist stably in the air. This top-notch joint system is located in the SLAC National Laboratory, right next to Stanford University.
Now this set of cutting-edge equipment is a powerful tool for studying the quasi-one-dimensional copper oxygen chain material system. The low-dimensional geometric structure of this material causes it to be very unstable. For bulk materials, only the undoped parent can exist more stably. Therefore, previous research on doping the next-dimensional copper oxygen chain has remained at the theoretical level [24-26]. But the films in this ultra-vacuum environment are different. Baking this film containing one-dimensional copper oxygen chains with ozone can change the density of carriers in the copper oxygen chain and can perform spectral measurements at the same time. Based on this idea, the research team conducted a systematic measurement of the material in order to obtain the information on doping of the one-dimensional system corresponding to the quasi-two-dimensional copper oxide superconductor [3].
In-depth reading:
The movement of the airborne is mainly determined by t, while the movement of the spin sub is mainly determined by the energy of spin interaction J=4t2/U, so the movement speed of the airborne and spin sub is not the same. In the angle-resolved photoelectron spectrum (ARPES), two non-coinciding branches will be seen. However, in undoped systems, no information related to the interaction between carriers is seen in ARPES. The key to achieving controllable doping of copper oxygen chains in the experiment is the combination of film growth and ozone baking, which can controllable the oxygen content in the crystal lattice, and oxygen atoms provide holes to the system [36].
oxide film growth and synchronous radiation ARPES ultra-high vacuum interconnection is the key to the success of the experiment, and there are three reasons: (1) This compound is extremely sensitive to air and decomposes within a few seconds when it touches air; (2) ARPES measurement requires extremely high surface quality, and the deposits in the air will have a fatal impact on the spectral mass; (3) The photon energy required for measurement can be provided by synchronous radiation.
04 First discovery: Super nearest neighbor attraction
uses large scientific equipment to synchronize the light source. In the world's most advanced angle resolution photoelectron spectrometer, we can see the loophole (holon) and the interaction between the loopholes [3]. Specifically, there is a peak in the momentum distribution curve of the photoelectron spectrum, representing the intensity of the interaction between this hollows [37,38]. The red line shown in Figure 5 is an experimental curve measured in the one-dimensional copper oxygen chain. The two in the middle are the main peaks representing the loopholes, and there are obviously a pair of strong "shoulders" on both sides. This "shoulder" is the characteristic peak of the interaction between the loopholes.
Figure 5
In a one-dimensional system, computer theoretical numerical simulation can give accurate predictions of different theoretical models. We see that in the prediction curve given by the pure Hubbard model, the shoulder characteristics are particularly weak and almost invisible, which obviously cannot match the experiment. If the Hubbard model is based on the Nearest Repulsion (simulating the long-range electrostatic Coulomb interaction between electrons) , even if the repulsion is very strong, the strength of the shoulder cannot be strengthened.But on the contrary, if you are based on the Hubbard model and the strong attraction of the neighbors, it will be very consistent with the experimental curve!
The nearest neighbor has a very strong attraction. Based on the mathematical form of spin charge separation in Hubbard's model itself, we can actually derive the effective attraction between a loophole. However, the attraction found in the experiment is ten times the intensity of the nearest neighbors included in the Hubbard model! Not only that, this experiment also systematically measured copper oxygen chains of different doping degrees, and the theoretical prediction of strong attraction of nearest neighbors of the same intensity was very well matched with all experimental spectral lines!
This shows that in real copper oxide, there is a strong near-neighbor attraction, and the source of this attraction is outside the Hubbard model. Since the structure of quasi-one-dimensional copper oxygen chain and quasi-two-dimensional copper oxygen surface is very similar, the one-dimensional quantum microscopic theoretical model can be generalized to 2D after certain corrections. The "Hubbard + Nearest Neighbor Attraction" model in the paper is based on the great success of the Hubbard model itself. Coupled with the newly discovered evidence of super nearest neighbor attraction, it helps with high-temperature superconducting electron pairing. We believe that this may be a complete theoretical model describing high-temperature superconductors!
In-depth reading:
ARPES can measure the kinetic energy and momentum of photoelectrons at the same time. Due to the energy conservation law of momentum inversely elicits the energy and momentum information of electrons in materials. Figure 5 shows the momentum distribution curve of binding energy below a certain Fermi surface. In one-dimensional strongly correlated electronic systems, the behavior of electrons affects each other and physically reflects more collective characteristics than individual characteristics. Therefore, the spectral lines of ARPES will usually become wider than those of higher dimensions.
theoretical numerical simulation can accurately calculate the spectral function of a one-dimensional system and compare it with ARPES data one by one, so a more accurate conclusion can be drawn. The attraction of this neighbor can be expressed as V~-t, which is ten times greater than the effective attraction intensity V~-0.1t generated by the Hubbard model itself through low energy projection.
05 Possible sources of super nearest neighbor attraction: Phonon
So what is the source of attraction between this electron and electron (or holes and holes) ? There should not be a mutually attractive electrostatic force between the positively charged holes.
People often say that they don’t know the true face of Mount Lu because they are in this mountain. If we only consider the electrons in solids, of course it is impossible to attract each other. But don't forget that the whole solid is electrically neutral, in addition to electrons, there are also positively charged metal cation (here "yang" means positively charged) The positively charged background formed by the lattice. Since the cations also move slightly, the electrons are actually moving in a positively charged grid that can vibrate!
Solid Physics , we mathematically describe the weak vibration of cations as a kind of quasi-particle : when there is no vibration, it means that this quasi-particle is not produced, and an increase in the amplitude means that the number of such particles increases. This quasi-particle is called phonon . When we consider the attraction between phonon (lattice vibration) and electrons, we will find that phonons can serve as a medium to generate attraction between electrons!
Imagine that you throw glass balls on a flat plate, and these glass balls will be scattered everywhere due to the collision between balls, which is similar to the case of pure electronic systems. But if we throw glass balls on the soft mattress, you will find those balls gather together. This is because when one ball presses the mattress out of a pit, the second ball will tend to fall into the pit to reduce potential energy. If we only care about the position of the balls and ignore the background of the mattress, it looks like these glass balls are attractive to each other.
Similarly, the vibration of the lattice composed of cations in a solid will induce an attraction between electrons like a mattress.This interaction between lattice vibration and electrons, we call electrophonon coupling, is actually the mechanism of conventional metal superconducting! Badin , Cooper and Schrief won the 1972 Nobel Prize in Physics [39] for creating this theory (named "BCS Theory" after them) .
Using this phonon as the media attraction mechanism, can we explain the nearest neighbor attraction found in the copper oxygen chain? It can be proved in theory that when the frequency of phonon (that is, lattice vibration) is very high, this interaction only exists between different electrons of in the same unit cell (the so-called unit cell is a unit of the lattice, and the unit cell periodically is the lattice) ; but when the frequency gradually decreases, this interaction can extend to a longer distance.
also uses glass balls and mattresses as an example: imagine that glass balls are constantly moving on the mattress. If the recovery speed of the mattress is very fast, then after a glass ball rolls over, the deformation of the mattress will immediately recover, and the glass balls moving from a distance will not feel the pit left by the former; only when the recovery speed of the mattress is much smaller than the movement speed of the glass balls, this pit potential energy can be transmitted to other glass balls farther away. Based on this principle, we quantitatively analyze the known electrophonon coupled intensity and possible near-neighbor attraction interactions. Unfortunately, this value is much smaller than the intensity of the attractiveness we need. Is
a problem with the theoretical model, or is there a more complex degree of freedom at work? This problem has troubled physicists for a long time. After re-examining the entire logical framework, we may be influenced by the ideas of conventional superconducting BCS theory. It is generally believed that the coupling of electrophonons must be the strongest when the distance is closest, and rapidly decays with distance. Therefore, generally speaking, only coupling at the same unit cell position is considered and other farther situations are ignored. The physical properties of conventional superconducting materials estimated from this are also basically consistent with the experimental results.
However, for copper oxides, since the Hubbard model has revealed that there is extremely strong repulsion at the same unit cell position, what should be more concerned about is the electron interaction between two adjacent unit cell positions. Naturally, the main contribution of this near-neighbor unit cell interaction should not come from the electrophonon coupling within the unit cell, but the electrophonon coupling between the unit cells. Based on this idea, supplemented by the latest developed non-Gaussian state precision diagonalization method [40], the research team analyzed the impact of long-range electrophonon coupling on this effective attraction. As expected, its contribution is much greater than the aforementioned estimate that only considers the electrophonon coupling in the unit cell. Moreover, the intensity of this effective attraction is very consistent with the experimental results [41].
Of course, the above discussion on the source of attractiveness of this nearest neighbor is only a theoretical explanation and prediction. A more stringent conclusion still requires further experimental analysis of in different copper oxides (especially in high-temperature superconducting materials). It is worth emphasizing that if the above mechanism is ultimately proven to be correct, electrophonon coupling will become the last step in solving the problem of high-temperature superconducting, but its mechanism of action is completely different from that of traditional BCS superconducting, and the apparent phenomena generated are also very different.
In high-temperature superconducting materials, the strong correlation effect between electrons is still the most significant phenomenon. Therefore, it is the mutual cooperation and competition between strong electron correlation and electrophonon coupling that creates this strange physical phenomenon. Because these two interactions are widely present in materials, it may contain richer physics and more valuable applications. The theoretical models, numerical technologies that have flourished in recent years, as well as the constantly improved experimental methods and characterization accuracy, are expected to rapidly advance research in this direction.
In-depth reading:
Phonons can be quadratic quantized to describe more microscopic, quantized vibration patterns. This mechanism of mutual attraction was actually proposed and verified in the middle of the last century.When this attraction is strong enough, electrons tend to exist and move in pairs, forming a new bound state: Cooper pair. This pair of electrons presents the properties of bosons and therefore are not scattered in motion, reflecting superconductivity. This theory is one of the most famous discoveries in solid physics: BCS theory. It successfully explains the superconducting phenomenon of most substances at low temperatures. Later, after various improvements to different degrees, the description of the superconducting phenomenon was improved from qualitative to quantitative magnitude [42-45]. The electron pairing mechanism in
copper oxygen superconductor is different from that of traditional BCS superconductors, and the phenomena produced are also different. For example, Cooper pairs in copper oxygen superconductors show d-wave symmetry, rather than s-wave symmetry. The parent body of the superconductor is an antiferromagnetic insulator. Through the non-Gaussian precise diagonalization method, if we bring in the known electrophonon coupling intensity and phonon frequency, and consider the coupling effect naturally attenuates with distance according to the law of electromagnetic force, the long-range electrophonon coupling gives the intensity of this effective attraction interaction, which is exactly V=-t, which is completely consistent with the experimental results.
06 Outlook: How to design a higher temperature high-temperature superconductor
So far, through experimental and theoretical comparisons, we not only found an important evidence of an important ultra-strong nearest electron attraction interaction that has been ignored before, but also quantitatively explained at the microscopic level that this interaction may originate from phonons. Although phonons seem to play an important role in both conventional superconductors and copper oxide superconductors, it does not mean that we are back to the simple explanation of the superconducting of electrophonon coupling.
We have actually reached a deeper understanding of high-temperature superconducting pairing, the most profound quantum mechanics problem in today's era: electron-electron interaction and electron-phonon interaction work together to create these wonderful physical phenomena in strongly related electronic systems. Of course, it may be necessary to complete this story more direct experimental evidence and theoretical calculation efforts, but we may be about to reach the ending. Behind this seemingly simple story, it actually contains a large number of innovations in experimental techniques and theoretical numerical methods from the scientific community. Scientific discoveries often do not rely on inspirational ideas, but are more about the improvement and iteration of instruments, materials, algorithms, and models.
high-temperature superconducting mechanism is a topic that is no longer young. In the process of two to three generations of people continuously charging them, the exploration of the final mechanism is of the top priority, but the technological innovations generated in this process cannot be ignored.
For example, in terms of experiments, a variety of characterization technologies represented by angle resolution photoelectron spectrometer (ARPES) have made great progress in the research of high-temperature superconducting, and later shines in the research of topological materials. In terms of theory, computational physics methods represented by density matrix reforming groups closely combine physical theory with modern scientific computing technology, greatly deepening our understanding of cutting-edge problems such as quantum entanglement. Of course, other slight improvements and even failed attempts in experiments, theory, numerical aspects are solidifying our inspiring ideas into knowledge that has been tempered.
Understanding the mechanism of high-temperature superconductors is not only of great scientific significance, but also hopes to design high-temperature superconductors with higher transition temperatures based on these scientific understandings, and finally be implemented experimentally. If the materials at room temperature (that is, 300K, equivalent to 27℃) and normal pressure (that is, a standard atmospheric pressure) can be superconductive and conductivity can be without resistance, and the entire human society based on the electrical industry will undergo tremendous changes.
Based on the current understanding of the mechanism of high-temperature superconductor, can higher-temperature superconductors be designed? The answer is: We are already on the way!
We have realized that the Hubbard model provides a platform for basic electronic systems, and the key to high-temperature superconducting pairing may be due to the strong near-neighbor attraction brought by phonons. In this way, if we want to obtain stronger near-neighbor attraction, we need to further optimize the phonon mode and the electron phonon coupling strength.
A possible solution is to combine the two-dimensional copper oxygen surface with a charge bank with a better phonon frequency through a heterojunction, which in principle should further increase the superconducting transition temperature. In terms of specific implementation, there is still a lot of work to be done in material engineering for copper oxide high-temperature superconductors, but for another type of high-temperature superconductor - iron-based superconductors, there have been some delightful attempts [47-49].
Even based on existing copper-based high-temperature superconducting materials, the industrial application of high-temperature superconducting has gradually entered a good state. It has broad development prospects in the fields of strategic technology (such as high-temperature superconducting controlled nuclear fusion and the new generation of high-energy particle accelerator), , transportation (such as high-temperature superconducting magnetic levitation trains and ship motors), , medical (such as ultra-high resolution nuclear magnetic resonance imaging and quantum interference cardioencephalography), , electric power (such as high-temperature superconducting energy storage devices, cables, fault current limiters, transformers, generators), , communication (such as high-temperature superconducting microwave filters, oscillators, single-photon detectors and terahertz detectors) and other fields.
In short, it has been 34 years since the research on high-temperature superconductivity. Although there are still many unsolved mysteries, humans have become more and more deeply aware of it. Therefore, they have also made more extensive developments in important disciplines such as quantum multibody physics, quantum materials, quantum chemistry, etc. step by step. The mechanism of high-temperature superconducting is still the jewel in the crown of condensed matter physics, but the moment humans really take it off should not be too far away.
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