Boltzmann equation and semi-classical magnetoconductivity in Weyl semimetal

Abstract

Weyl semimetal is a kind of three-dimensional material which has several band touch points in the energy band structure. These band touch points are called Weyl nodes, which are associated with a quantity called chirality. Near each Weyl node, the behaviour of electrons can be described by Weyl equation. Weyl nodes can be regarded as monopoles in momentum space with charges ±1. Due to the fermion doubling theorem, each Weyl node should be paired with another node with opposite chirality. For a single Weyl node, the number of charges is no longer conserved in the presence of paralleled electric and magnetic field. This phenomenon is called chiral anomaly. Chiral anomaly will lead to some novel transport phenomena such as negative magneto-resistance and chiral magnetic effect. Weyl semimetal also has novel surface states which are called Fermi arcs. TaAs is the first kind of Weyl semimetal material which is discovered in experiments. Fermi arcs and negative magneto-resistance have been observed in TaAs. This work focuses on magneto-resistance of Weyl semimetal systems. In contrast with quantum limit, we consider the case which Boltzmann equation can be used in calculation. To solve the Boltzmann equation, we use the relaxation time approximation to deal with the collision term. Then the collision term is divided into two parts, which describe both intra- and inter-node scattering respectively. With the solution of Boltzmann equation, we can get the analytical expression of the conductivity. Modifications of orbital magnetic moment and classical cyclotron motion term are considered in this work. This calculation gives a longitudinal conductivity which is proportional to B^2, which is coincided with previous theories.