Nonequilibrium Excitations and Transport of Dirac Electrons in Electric-Field-Driven Graphene

TL;DR

This paper studies how charge-neutral graphene responds to strong electric fields, revealing unique nonequilibrium excitations and transport behaviors that match recent experimental observations and suggest potential infrared device applications.

Contribution

It provides a detailed theoretical analysis of nonequilibrium electron-hole excitations and transport in graphene under electric fields, highlighting the role of optical phonons and Landau-Zener tunneling.

Findings

Electron-hole excitations follow a superlinear IV relation $I \,\propto \,E^{3/2}$.

Steady-state current becomes marginally sublinear $I \,\propto \,E$ due to optical phonon dissipation.

Doping away from the Dirac point leads to current saturation and semi-classical velocity behavior.

Abstract

We investigate nonequilibrium excitations and charge transport in charge-neutral graphene driven with DC electric field by using the nonequilibrium Green's function technique. Due to the vanishing Fermi surface, electrons are subject to non-trivial nonequilibrium excitations such as highly anisotropic momentum distribution of electron-hole pairs, an analog of the Schwinger effect. We show that the electron-hole excitations, initiated by the Landau-Zener tunneling with a superlinear IV relation $I \propto E^{3/2}$, reaches a steady-state dominated by the dissipation due to optical phonons, resulting in a marginally sublinear IV with $I \propto E$, in agreement with recent experiments. The linear IV starts to show the sign of current saturation as the graphene is doped away from the Dirac point, and recovers the semi-classical relation for the saturated velocity. We give a detailed discussion on the nonequilibrium charge creation and the relation between the electron-phonon scattering rate and the electric field in the steady-state limit. We explain how the apparent Ohmic IV is recovered near the Dirac point. We propose a mechanism where the peculiar nonequilibrium electron-hole creation can be utilized in a novel infra-red device.