Basis-Independent Spectral Methods for Non-linear Optical Response in Arbitrary Tight-binding Models

TL;DR

This paper introduces a basis-independent perturbative approach using the Keldysh formalism and Kernel Polynomial Method to efficiently compute non-linear optical responses in arbitrary, non-translation-invariant tight-binding models, demonstrated on disordered graphene.

Contribution

It presents a novel basis-independent perturbative method for non-linear optical response calculations applicable to arbitrary tight-binding models, including disordered systems.

Findings

Successfully computed second-order optical conductivity for disordered graphene.

Demonstrated the method's efficiency for non-translation-invariant systems.

Validated the approach with proof-of-concept results on gapped graphene with vacancies.

Abstract

In this paper, we developed a basis-independent perturbative method for calculating the non-linear optical response of arbitrary non-interacting tight-binding models. Our method is based on the non-equilibrium Keldysh formalism and allows an efficient numerical implementation within the framework of the Kernel Polynomial Method for systems which are not required to be translation-invariant. Some proof-of-concept results of the second-order optical conductivity are presented for the special case of gapped graphene with vacancies and an on-site Anderson disordered potential.