Diffusion of Dirac fermions across a topological merging transition in two dimensions

TL;DR

This paper investigates how Dirac fermions in two dimensions transition from a semi-metallic state to a gapped phase through a merging transition, analyzing the resulting anisotropic transport properties using Boltzmann and Kubo formalisms.

Contribution

It provides a detailed theoretical analysis of transport properties across a topological merging transition in 2D Dirac systems, highlighting anisotropic effects and semi-Dirac spectrum characteristics.

Findings

Transport becomes highly anisotropic near the transition

The Dirac nature influences the anisotropic self-energy

Conductivity tensor reflects the semi-Dirac spectrum features

Abstract

A continuous deformation of a Hamiltonian possessing at low energy two Dirac points of opposite chiralities can lead to a gap opening by merging of the two Dirac points. In two dimensions, the critical Hamiltonian possesses a semi-Dirac spectrum: linear in one direction but quadratic in the other. We study the transport properties across such a transition, from a Dirac semi-metal through a semi-Dirac phase towards a gapped phase. Using both a Boltzmann approach and a diagrammatic Kubo approach, we describe the conductivity tensor within the diffusive regime. In particular, we show that both the anisotropy of the Fermi surface and the Dirac nature of the eigenstates combine to give rise to anisotropic transport times, manifesting themselves through an unusual matrix self-energy.