Microscopic analysis of relaxation behavior in nonlinear optical conductivity of graphene

TL;DR

This paper develops a quantum master equation approach to analyze the nonlinear optical conductivity and relaxation dynamics in graphene, accounting for interactions with phonons and electrons in a dissipative quantum framework.

Contribution

It introduces a general formulation for nonlinear interband optical conductivity in graphene using a spin-Boson model and quantum master equations, including effects of a quantum bath and finite temperature.

Findings

Population inversion in steady state under nonlinear excitation

Interband coherence characterized by a single dimensionless parameter

Method applicable to doped and gapped graphene at finite temperatures

Abstract

We present here a general formulation for the interband dynamical optical conductivity in the nonlinear regime of graphene in the presence of a quantum bath comprising phonons and electrons. Our main focus is the relaxation behavior of the quantum solid of graphene perturbed by an oscillatory electric field. Considering the optical range of the frequency and a considerable amount of the amplitude of the field, one can observe a nonlinear response by formulating a quantum master equation of the density operator associated with the Hamiltonian encapsulated in the form of a spin-Boson model of dissipative quantum statistical mechanics. Mapping the valence and conduction states as the eigenstates of the Pauli spin operators and utilizing the rotating wave approximation to omit off-resonant terms, one can solve the rate equation for the mean population of the conduction and valence states and the mixing matrix elements between them. Our results reveal the nonlinear steady-state regime's population inversion and interband coherence. It is characterized by a single dimensionless parameter that is directly proportional to the incident field strength and inversely proportional to the optical frequency. Our method is also capable of calculating the nonlinear interband optical conductivity of doped and gapped graphene at finite temperatures. The effects of different bath spectra for phonons and electrons are examined in detail. Although our general formulation can address a variety of nonequilibrium response of the two-band system, it also facilitates a connection with phenomenological modeling of nonlinear optical conductivity.