Ballistic transport in graphene beyond linear response

TL;DR

This paper models ballistic transport in graphene under strong electric fields, revealing nonlinear current behavior, pair creation dynamics, and Bloch oscillations beyond linear response.

Contribution

It provides a quantitative analysis of particle-hole pair creation and current evolution in graphene beyond linear response using the tight binding model.

Findings

Current is linear in E for short times

Current increases and exhibits Bloch oscillations at longer times

Pair creation rate deviates from Schwinger formula in certain regimes

Abstract

The process of coherent creation of particle - hole excitations by an electric field in graphene is quantitatively described beyond linear response. We calculate the evolution of current density, number of pairs and energy in ballistic regime for electric field E using the tight binding model. While for small ballistic flight times the current is linear in E and independent of time, for larger ballistic times the current increases and finally at yet larger times Bloch oscillations set in. It is shown that the number of pairs follows the 2D generalization of the Schwinger's creation rate only on certain time segments with a prefactor different from that obtained using the asymptotic formula.