Microscopic Green's function approach for generalized Dirac Hamiltonians

TL;DR

This paper introduces a general analytical method to compute microscopic Green's functions for Dirac materials, aiding the understanding of their transport properties at atomic scales.

Contribution

The authors develop a versatile analytical approach to calculate Green's functions for Dirac materials with various edge types and geometries, enhancing modeling capabilities.

Findings

Derived analytical formulas for density of states and scattering probabilities.

Validated method on germanene and transition metal dichalcogenides.

Provided tools for interpreting transport experiments in Dirac materials.

Abstract

The rising interest in Dirac materials, condensed matter systems where low-energy electronic excitations are described by the relativistic Dirac Hamiltonian, entails a need for microscopic effective models to analytically describe their transport properties. Specifically, for the study of quantum transport, these effective models must take into account the effect of atomic-scale interfaces and the presence of well-defined edges while reproducing the correct band structure. We develop a general method to analytically compute the microscopic Green's function of Dirac materials valid for infinite, semi-infinite, and finite two-dimensional layers with zigzag or armchair edge orientations. We test our method by computing the density of states and scattering probabilities of germanene and some transition metal dichalcogenides, obtaining simple analytical formulas. Our results provide a useful analytical tool for the interpretation of transport experiments on Dirac materials and could be extended to describe additional degrees of freedom like extra layers, superconductivity, etc.