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School of Physics Makes Progress on Weak Topological Insulator & Weyl Semimetal

Translator: News Agency of BIT  Lai Hongdi

Editor: News Center of BIT  Zhao Lin


     Recently, Professor Yao Yugui and his research team from the Laboratory for Quantum Design and Application of Functional Materials of Beijing Institute of Technology (BIT), have collaborated with Professor Zhang Fan of University of Texas at Dallas (UTD) and come up with the notion that the weak topological insulator and composite Weyl semimetal will be held stable in a specific kind of dynamics and can be realized in synthesized van der Waals materials, -- Bi4X4(X=Br, I). Related results have been published on Phys. Rev. Lett. (116, 066801 (2016)). This program received financial support from Excellent Youth Scholars program of BIT, Fundamental Research Foundation of BIT, National Natural Science Foundation of China and the Ministry of Technology.


     Discoveries of a series of quantum states, like this time with the topological insulator, are changing and deepening our basic knowledge towards quantum materials. Such kind of knowledge is likely to bring transcendent advantage for the technology application. For example, the topological insulator has an important significance on helping understand the controllable quantum phase transition of the topological insulator and the calculation of the number of topological quantum on Majorana base in the surface of spin-momentum locking state. The 3-dimensional topological insulator will need 4 topological indexes to describe (0; 1 2 3). If the first index is not 0, this topological insulator is considered to be a strong topological insulator. If the first index is 0 and the rest of the indexes are not all 0s, then it is considered to be a weak topological insulator. Furthermore, the strong topological insulator has an odd number of Dirac surface states while the weak topological insulator has an even number of Dirac surface states. It is worth mentioning that strong and weak topological insulators were both predicted by theory first, and then the strong topological insulator was confirmed by experiments. The strong topological insulator is the one now researched and understood the most, as the majority of strong topological insulators are layered materials, which makes it easy to observe the number of surface Dirac cones on cleavage surface, without going through the special surface passivation procedure.


    However, it is rather surprising that so-far there is no experiment having the luck finding the weak topological insulator. Scientists are now thinking that through stacking 2-dimensional topological insulators, they might be able to obtain the weak topological insulator. But, the problem with this method is that the characteristic surface Dirac cone can only be observed from its side instead of its cleavage plane on which actually has no characteristic surface state. Moreover, the non-cleavage plane not only is hard to obtain and stabilize, but has many dangling bonds, bringing the experiment with great challenges. Therefore, finding a new reaction system would help a great deal with the experiment verification and uncover of the properties of weak topological insulator. 


    Based on the previous research on the 2-dimensional large energy gap topological insulator, recently, Dr. Liu Chengcheng, Dr. Zhou Jinjian, Professor Yao Yugui, collaborated with Professor Zhang Fan came up with the notion that the weak topological insulator and composite Weyl semimetal can be easily realized in synthesized van der Waals materials, ¬-Bi4X4(X=Br, I).


    As figure 1 shows, the basic building block of this kind of materials is 1-dimensional atomic chain. What’s more, the planes, (100) and (001) namely,  vertical to the atomic chain are actually Cleavage planes. The intrinsic ¬-Bi4Br4, ¬-Bi4I4 are respectively the weak topological insulator and the strong topological insulator. The research team also discovered that uniaxial strain could incur topological phase transition. What’s more, in different strain zones, there is strong topological insulator, weak topological insulator, and normal band insulator, as is shown in figure 3. For the weak topological insulator, there are two anisotropy surface Dirac cones istead of topological surface state on the (100) cleavage plane, shown in figure 2. Also, when doing charge doping to the system, there will be four times Lifshitz transition on the surface state. As the cellular length of ¬-Bi4Br4, ¬-Bi4I4 multiplies along the c direction, relatively high symmetry points all have conducted anti-band for two times, hence becoming the topological mediocrity band insulator. It is worth noting that, as is shown in figure 4, the transition from weak topological insulator to strong topological insulator at the same time jeopardize the inverse symmetry of the system, creating a brand new Weyl semimetal phase or, that is, a Fermi arc between two cleavage planes. However, the Fermi arc is only on the (100) cleavage plane, which is called the composite Weyl semimetal.


     As typical weak topological insulator, such kind of synthesized van der Waals materials, ¬-Bi4X4(X=Br, I), provides an ideal platform for many novel physical experiments. The system, when on average having the properties of U(1) symmetry, time reversal symmetry and translation symmetry, will make the weak topological insulator stable compared to disorder. If lacking any of that properties, new physical effects would be introduced. For example, helical dislocation and topological defects would sabotage translation symmetry, resulting in spiral edge state. Apart from that, magnetism would break the time reversal symmetry, leading to the Hall Effect of anomalous quantum. Adjacent coupling induction of superconductor would jeopardize the U(1) symmetry, making the topological superconductor with Majorana zero mode.


Figure 1.crystal structure.(010) plane has Space inversion symmetry


Figure 2. (a)(b) No spin orbit coupling band structure of ¬-Bi4I4
(c) (001) surface state of ¬-Bi4I4
(d)(e) No spin orbit coupling band structure of ¬-Bi4Br4
(f) (100) surface state of ¬-Bi4Br4
(g) Lifshitz transition of (001) surface state of ¬-Bi4Br4
(h) A sketch of the stacking of ¬-Bi4Br4


Figure 3.  Topological phase transition caused by uniaxial stress


    Figure 4. (a) composite Weyl semimetal can be found among the phase change between strong and weak topological insulators. Weyl semimetal can be found when topological phase transition happened between strong topological insulator and band insulator.
                    (b) Fermi arc of composite Weyl semimetal on (001) cleavage plane
                    (c)coexisting Fermi arc and Fermi circle of composite Weyl semimetal on (100) cleavage plane





Release date:2016-06-02