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exchanges academics, and occasionally, with the development of topological energy band theory, more and more new particles are discovered in condensed matter material systems. It has received widespread attention because it has unique massless chiral Weyl fermions in Weyl semi-metals and may be used in new electronic information devices in the future. Recently, the research team of Miao Feng of Nanjing University has made important progress in the research on the transport characteristics of the second category of Weil semi-metals. Related articles have been published in Nature Communications recently. Through this article, we will give readers a basic introduction to the background and content of the work.
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Strange "chial" fermion : Weil fermion
Objects in the macroscopic world are usually moving at a lower speed, and these objects can all be described by Newtonian mechanics. However, when we narrow the scale to molecular, or even atomic scales, Newtonian mechanics no longer apply. At this time, a group of great scientists came up with a new solution - quantum mechanics to solve such problems. The basis of microscopic and low-speed quantum mechanics is the Schrödinger equation, just as Newton's second law is the basis of Newton's mechanics. When the development of quantum mechanics encountered a bottleneck of "high speed", Paul Dirac borrowed Einstein's special theory of relativity and introduced the concept of "high speed" into Schrödinger's equation, and obtained the Dirac equation. This equation describes Dirac fermion , which considers the relativity effect.
Later, German physicist Hermann Weyl theoretically proposed a new pair of particles with a static mass of 0 (such as photons in high-energy physics ) and satisfies the Dirac equation, which is called Weilfermion. Interestingly, this pair of Weilfermions also has the characteristics of "chiralization". They are so similar to the left and right hands of humans, but they are mirror-symmetrical. One of the Weylfermions has the same "axis of rotation" direction as its direction of motion, while the other is opposite, and they can be said to have "right-hand" and "left-hand" chiral signs, respectively.
The usual fermions cannot distinguish between "left-hand" and "right-hand" chiral signs. So can we realize Weil fermions in a certain system and separate the two chiral signs of Weil fermions from each other?
Figure 1: Chiral different fermions (green left-handed sign, blue right-handed sign)
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Wiler semi-metal: Weil fermions vector
Wilderness things will never be easily implemented. The theoretical prediction of Welsh fermions is the speed of light and has a relativistic effect. People initially searched for Welsh fermions in high-energy physics. Neutrino was once considered Weil fermions, but later it was discovered that neutrinos had mass, and the road to finding Weil fermions became even more bumpy.
theory predicts that nearly 80 years later, the development of topological energy band theory in condensed matter physics has brought new hope to people. In solid materials, the movement of electrons is affected by the lattice periodic potential field, and is also affected by the interaction of other electrons. In some special lattices, the collective behavior of electrons can be described as a new "quasi-particle". Subsequent research found that in some solid materials, the conduction band and the valence band can intersect at one point in the energy band. If quasi-particles are used to compare particles in quantum field theory and high-energy physics, then low-energy quasi-particles that satisfy linear dispersion relationships at intersections can magically satisfy the relativity effect. The initially discovered topological insulator surface states, graphene, and quasi-particles at Dirac points in three-dimensional Dirac semi-metals all belong to Dirac fermions. As mentioned earlier, Dirac fermions are actually composed of two opposite Weil fermions in combination and superposition at the same point in the momentum space. To achieve the separation of the two in the momentum space, it is necessary to break the symmetry of time or space inversion. Applying a magnetic field or adding magnetism can destroy the temporal inversion symmetry, but because magnetism will affect the experimental observation of the Weil point, it is not easy to confirm the existence of Weil fermions.In recent years, scientists have finally discovered Weil fermions in solid materials that destroy spatial inversion symmetry, and the corresponding material is called Weil semi-metal. Chinese scientists have made many breakthrough contributions in the discovery of Welfermions.
In Weil semi-metals, the opposite Weil points in the momentum space are located at different positions. The two always appear in pairs, which can be regarded as " magnetic monopole ". Separated Weil fermions give Weil semimetals many novel physical properties. In addition, the two Weil points are not irrelevant, and they are connected to each other through the surface state of Weil semimetal; this surface state is an unclosed curve with topological protection, called the Fermi arc.
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Class II Weil semi-metal
Ideally, we always expect that the excited states in Weil materials are all Weil fermions, but the actual materials are often not the case, because Weil fermions only exist at some discrete Weil points in the energy band. The energy band near the Weil point is a "cone" similar to the "X-shaped". In a class of Weil semimetals that were initially discovered, these "cones" are approximately "upright", and the Weil points satisfy Lorentz invariance, that is, the momentum of each lattice is equivalent (determined by the Lorentz metric). This type of semi-metal is represented by the TaAs compound discovered by the Institute of Physics of the Chinese Academy of Sciences and is called the first type of Weil semi-metal.
In the wonderful condensed matter physical world, the energy bands are always changing. Changing the lattice structure, atomic species, and even adding some perturbations may cause huge changes to the bands. People have also found that in some materials, the "cone" near the Weil point can undergo severe inclination. The severe band tilt causes the Fermi surface to produce electronic pockets and hole pockets, and the Weil point is the intersection of these two pockets. Because the band tilt destroys the uniformity of the momentum space, it violates Lorentz invariance. This type of material is called the second type of Weil semi-metal, and immediately attracted great attention after theoretical predictions. The first Weyl semi-metallic material to be predicted is WTe2, and then a variety of materials are predicted (MoTe2, etc.). Observing the energy band structure and surface state Fermi arc is the most direct means to verify the second category of Weil semi-metals. The Fermi arc in WTe2 is not easily observed accurately because its scale is smaller than the experimental resolution of the angular resolution photoelectron spectrometer (ARPES). In comparison, the Fermi arc in MoTe2 materials is more easily observed. At present, some research groups have used ARPES to conduct experimental verification and have achieved important results (representative results include the recent work published by the Tsinghua University research group).
Figure 2: Two types of energy bands around Weil points, upright cone (first class Weil points), and inclined cone (second class Weil points).
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Chiral transport characteristics: Exploring the "chiral transport Electronics "
The second category of welter fermions has attracted great attention is its unique "chiral" characteristics. Although the existence of the second category of welter points can be verified through energy band calculation and angle-resolved photoelectron spectroscopy research, it is of great research significance to experimentally verify the chiral transport characteristics of such fermions and further realize field regulation.
Weil semi-metal, whether in the first or second category, is predicted to have a strange electron transport characteristic, namely, the negative magnetoresistance effect, that is, the resistance will decrease after the external magnetic field is applied. In general non-magnetic materials, electrons will deviate from forward under the Lorentz force of the magnetic field, so the resistance will usually increase, resulting in positive magnetoresistance rather than negative magnetoresistance. Therefore, this negative magnetoresistance effect is an important exclusive transportation feature of Weil semi-metals and an important indicator for transport experiments to verify Weil semi-metals. The mechanism for producing negative magnetoresistance comes from the "magnetic monopole" of chiral Weil fermions at Weil point. This "magnetic monopole" only exists in the momentum space, and the corresponding "magnetic field" generated is called Berry curvature. Under the influence of this strange Berry curvature, the semi-classical movement of electrons in Weil semi-metals will be corrected, resulting in a series of strange effects, such as chiral anomalies, abnormal Hall effect, chiral magnetoelectric effect, etc. Negative magnetoresistance is probably one of the most intuitive effects.In particular, the negative magnetoresistance comes from the "magnetic monopole" of the Weil point, so the closer it is to the Weil point, the stronger the negative magnetoresistance should be. Observing this relationship is the key to verifying the existence of Weil fermions in the transportation experiment.
Figure 3: Chiral opposite Weil dots can be regarded as magnetic monopole
In addition, for the first and second Weil semimetals, the difference in the two can lead to a huge difference in the negative magnetoresistance effect. For the first type of Weil semi-metal, the negative magnetoresistive effect can be observed in all directions of space; for the second type of Weil semi-metal, the negative magnetoresistive has a strong anisotropy , which can only be observed in special directions, and the negative magnetoresistive will disappear in other directions and have positive magnetoresistive. Therefore, observing the anisotropy of negative magnetoresistance is also a key evidence to judge the existence of the second type of Weil points in transportation experiments.
Figure 4: Fermi can adjust in situ near the second category of Weil points
This time, the research team of of Nanjing University School of Physics observed the negative magnetoresistance effect corresponding to the second category of Weil semimetal in a high-quality WTe2 film for the first time, which is consistent with previous theoretical expectations. At the same time, in order to verify the relationship between negative magnetoresistance and the "magnetic single pole" of Weil point, the research team took advantage of the advantages of thin-film devices to introduce external field gate voltage adjustment, realizing the in-situ regulation of Weil semi-metal Fermi energy near Weil point for the first time. The negative magnetoresistance effect reaches a maximum value during the adjustment process, which strongly shows that Fermi can pass through the Weil point. This series of observations provides sufficient evidence for verifying that WTe2 is a second class of Weil semimetals. Moreover, this is also the first time for all currently known first and second types of Weil semimetals, the electron transport experiment of controlling gate voltage through Weil points is realized. This work not only provides a universal experimental method for in situ study of the second type of Weilfermions in condensed matter physics, but also has important significance for topology and application research of chiral electrons. Professor Miao Feng of Nanjing University, Professor Wan Xiangang and Professor Wang Bogen, who provide theoretical calculations, are co-corresponding authors of the paper, Academician Xing Dingyu of Nanjing University and Professor Lu Haizhou of Southern University of Science and Technology, also provided theoretical support for the research, and Professor Wang Zhenlin of Nanjing University and provided Raman experiment assistance.
Chiral Weil fermions is a novel particle. Studying its transport characteristics and transmission mechanisms may bring us into the research field of "chiral electronics". At the same time, massless Weyl fermions are also of great significance to achieving low-energy transmission devices.
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