Anomalous Properties On Weyl Semimetal

Recently topological insulators and Weyl semimetals, which have topological non-trivial momentum space topology have attracted considerable attention in condensed matter physics. The research on topological insulators and Weyl semimetals has been deepening our understanding of nature and the relation between condensed matter physics and high energy physics. In this thesis, after an introduction of basic physics on topo-logical insulators and Weyl semimetal, we shall focus mainly on the following topics:(1) We studied the project the periodic potential inducing the splitting of topolog-ical invariant-Chern number for bands in the condensed matter system. We found the relationship between Chern number of original bands and ones from new bands by the periodic potential. People always know the sum of their Chern numbers is equal to the original Chern number, but the exact number for each splitting band is unknown. In this thesis, we found that, in most general case one band is split two bands, the integral of the phase of the periodic potential around the new Brillouin zone also determines the values of new Chern numbers besides the original Chern number.(2) In this thesis, we introduce some basic theoretical results and experiments in this three dimensional nontrivial topological semimetal-Weyl semimetal. There are even numbers Weyl points separated in momentum and energy space in the bulk of Weyl semimetal. Each Weyl points can be viewed as a momentum monopole. There is gap-less surface states connecting the Weyl nodes in the bulk. The electric field can induce the anomalous Hall current in Weyl semimetal because of the separation of Weyl points in momentum space. But most amazing effect is the chiral magnetic effect (CME). The CME said that, even absence the electric field, the charge current can be induced directly by the external magnetic field with the same direction. These effects can be derived from the effective action after coupling to the electromagnetic field.(3) The elastic response can also be calculated to show the topological nontrivial physics just as the electromagnetic response. We studied the anomalous elastic response in three dimensional Weyl semimetal. We get the effective action, which including θ term and NY invariant, adapting the method by Fujikawa in chiral anomaly. We also found that there is the anomalous momentum current in Weyl semimetal induced by the dislocations as Burgers vector. And the physical meaning for this current and its application in condensed matter has also been discussed.(4) Based on the numerical results by the exact numerical diagonalization method, we first demonstrate the existence of the chiral magnetic effect in a general model of Weyl semimetal. As predicted by CME, there is the anomalous current induced by mag- netic field in the same direction. We have evaluated this current for various system sizes, magnetic field strengths, temperatures and the energy difference AE between different Weyl points. The current can be zero only when the energy difference AE=0. We also proved that only the states at the Fermi surface can contribute the current in the zero temperature limit. In the weak field limit, the anomalous current from the numerical result is proportional to the strength of magnetic field and the energy separation with a universal coefficient e2/h2, predicted in the theoretical work. We also discussed the reason of existence for this nontrivial current and its fundamental physics.