Disordered transport in topolotical semimetals

Abstract

Topological semimetals are novel materials with topologically non-trivial electronicstructures. In this study we focus on Weyl semimetals. A Weyl semimetalhas a gapless band structure where the conduction band and the valance bandare degenerate at a nite number of points. Near each of these band degeneratepoints, the dispersion is linear in all momentum directions and described by theWeyl equation. These points are called Weyl nodes. A Weyl node acts as amonopole of Berry curvature in momentum space and is assigned with a topologicalcharge of 1. Weyl semimetals posses various exotic transport properties. Ithas been reported that in the presence of short range Gaussian disorder, a Weylsemimetal has a quantum phase transition from semimetal to metal at a nitecritical disorder strength. Above the critical disorder strength, the conductivity of the system increases as disorder strength getting stronger, which is opposite toits behaviour in usual metals. Previous studies mainly focus on a single Weyl node.However, there is a "no-go" theorem saying that the total topological chargemust be zero in the Brillouin zone. Thus Weyl nodes must come in pairs withopposite charge. In this thesis we study the disordered quantum transport in aminimal continuum model containing a pair of Weyl nodes. The model allows usto explicitly taking into account internode scatterings eect. The Green's functiontechnique and the self-consistent Born approximation are used to calculatethe density of states and conductivity of the model. A quantum phase transitionfrom semimetal to metal is observed. The density of states and conductivity ofthe model have similar behavior as in a single Weyl node. We found that thecritical disorder strength is reduced as internode scattering become stronger. Theconductivity near the nodes is further enhanced above critical disorder strengthbut its behavior is not qualitatively altered by internode scatterings. Our resultscan be applied to systems with multiple pairs of Weyl nodes.