News Source: School of Physics

Translator: Li Jingyan, Yang Ruiguang, News Agency of BIT

Recently, Professor Yao Yugui’s team at the School of Physics, Beijing Institute of Technology in collaboration with researcher Zhou Jianhui at the Science Center for Strong Magnetic Field, Chinese Academy of Sciences, and Professor Zhou Shuyun at Tsinghua University, predicted and discovered the quasi-particles of Type-III Weyl Fermion in charge density wave material Ta2Se8I in the high temperature phase. The relevant results were recently published in the form of Letter in Physical Review B with the title of Type-III Weyl semimetals: (TaSe4) 2I. This work was highly valued by editors and was selected as Editors ' Suggestion.

Figure1: The diagram of three types of Weyl points

(a)Point type Fermi surface of Type-I Weyl semi-metal

(b)Electron-hole pocket type Fermi surface of Type-II Weyl semi-metal

(c)Electron(hole)-electron(hole) pocket type Fermi surface of Type-III Weyl semi-metal

(d)Crystal structure of Ta2Se8I

(e)The surface state of quadruple spiral on the 001 surface.

In 1929, Hermann Weyl, German mathematician and physicist, predicted the massless Weyl Fermion. After nearly a century of exploration, people haven’t identified the basic particle “Weyl Fermion” in the vacuum yet, so it was called “Ghost Particle”. Recently, with the rapid development of state of topological material and material physics, people have found a new way to achieve the “Weyl Fermion”—low energy quasi-particle excitation in solid materials. In solids, these quasi-particles follow the same motion laws as the corresponding basic particles, such as the Weyl Equation. Researchers have found out the quasi-particles of Weyl Fermion in various solid materials, showing many novel physical properties and potential applications in spintronics and quantum computation. Ulike in the field of high energy physics, further studies have found that in solid materials, the Weyl Cone can be tilted and lead to Fermi surfaces with completely different geometric structures. For example, the linear tilting term makes the Fermi surface of point type (Type-I Weyl point, as shown in Fig.1 (a)) change into the Fermi surface of contact between an electron pocket and a hole pocket (Type-II Weyl point, as shown in Fig.1 (b)). The Fermi surface is a basic and profound concept in condensed state physics. The superconductivity, density waves, magnetism, electrical transport and other properties of the system are closely related to the Fermi surface. Therefore, finding materials with novel topological and geometric properties of Fermi surfaces has become an extremely important cutting-edged topic in the study of topological state of matter.

Yao Yugui et al. found Type-III Weyl Fermion quasi-particles in the high-temperature phase of charge density wave material Ta2Se8I, which is a new kind of solid quasi-particles with characteristics of " three highs ": high temperature phase, high-count number and high order tilting term. In this work, Authors found that the crystal symmetry can induce second-order or even higher-order tilt terms in the Weyl quasi-particle motion equation. Different from the linear tilting term, the second order tilting term leads to a completely new third kind of Weyl Fermions in multiple Weyl semimetals (the count number is 2 or 3). It has a unique Fermi surface: the Fermi surfaces of the electron-electron or hole-hole pocket contacts at the same high-count Weyl point (Figure1(c)). It is worth pointing out that this second order tilting term is not dominant in linear Weyl equations but only in high-count Weyl semimetals. In addition, due to the lack of experimental evidence for high-counting semimetals, it has not been found in the past.

We can understand the formation of the novel Fermi surfaces in type-III Weyl points by a simple energy band diagram. Linear tilting term increases the energy of positive wave vector k, decreases the energy of negative wave vector k, thus forming the electron-hole pocket type of Fermi surfaces(as shown in Fig.1(b)). Nevertheless, second order tilting term can add or reduce the energy of positive and negative wave vector k simultaneously(which depends on the positive and negative properties of the coefficient of second order tilting term), resulting in electron-electron or hole-hole pocket type of Fermi surfaces(as shown in Fig.1(c)). Based on the generalized tilting term of Weyl points, the authors came up with an intuitive and clear physical mechanism to classify Type-I, Type-II and Type-III Weyl semimetals uniformly.

Angle-resolved photoemission spectroscopy experiments indicate that Ta2Se8I(Fig.1(d)) in the high temperature phase has the characteristic energy dispersion of type-III Weyl fermions. Furthermore, the authors found that second order tilting term can cause the up-turning of Landau levels and the splitting of chial landau levels of Type-III Weyl semimetal, which can both become indicative evidence of diagnosing Type-III Weyl semimetal during experiments. As a matter of fact, it has already been written into the solid physics textbooks that Ta2Se8I of low temperature phase is a classical charge density wave material, but people’s understanding of its topological properties of high temperature phase and Pyres phase transition mechanism is not clear enough. The work reveals the nature of Weyl semimetal in Ta2Se8I of high temperature phase for the first time and will provide theoretical direction for discussions of related novel physical mechanism (as shown in Fig.1(e)). Type-III Weyl fermion predicted by the work was also discovered in ferromagnetic material X2RhF6 (X="K," Rb, Cs) by another research group (Phys. Rev. B 102, 195104(2020)).

This work was supported by the National Key Research and Development Program of China (Grant No.2016YFA0300600), the National Natural Science Foundation of China (Grant No.11734003), and the Strategic Pilot Research Program of the Chinese Academy of Sciences (Grant No.XDB30000000).

Passage link: https://link.aps.org/doi/10.1103/PhysRevB.103.L081402