Theory of Conductivity of Chiral Particles

TL;DR

This paper evaluates the band-coherent Boltzmann equation approach for calculating conductivity in chiral particles, comparing it with Kubo formula results in multilayer graphene models to identify the most accurate method.

Contribution

It introduces a detailed comparison of Boltzmann and Kubo methods for chiral particles, highlighting the impact of principal value terms on conductivity calculations.

Findings

Best agreement with Kubo results occurs without principal value terms.

The Boltzmann approach can accurately predict conductivity when properly formulated.

Chirality significantly influences the conductivity in multilayer graphene models.

Abstract

In this methodology focused paper we scrutinize the application of the band-coherent Boltzmann equation approach to calculating the conductivity of chiral particles. As the ideal testing ground we use the two-band kinetic Hamiltonian with an N-fold chiral twist that arise in a low-energy description of charge carriers in rhombohedrally stacked multilayer graphene. To understand the role of chirality in the conductivity of such particles we also consider the artificial model with the chiral winding number decoupled from the power of the dispersion. We first utilize the approximate but analytically solvable band-coherent Boltzmann approach including the ill-understood principal value terms that are a byproduct of several quantum-many body theory derivations of Boltzmann collision integrals. Further on, we employ the finite-size Kubo formula with the exact diagonalization of the total Hamiltonian perturbed by disorder. Finally, we compare several choices of Ansatz in the derivation of the Boltzmann equation according to the qualitative agreement between the Boltzmann and Kubo conductivities. We find that the best agreement can be reached in the approach where the principle value terms in the collision integral are absent.