Time-dependent transport in graphene nanoribbons

TL;DR

This paper models the time-dependent ballistic transport in graphene nanoribbons after a sudden bias, revealing transient behavior and steady-state conductivities that match known graphene and nanoribbon properties.

Contribution

It provides a theoretical analysis of transient and steady-state transport in graphene nanoribbons under a sudden bias, highlighting the evolution of conductivity over time.

Findings

Transient current exhibits a plateau with minimal conductivity of graphene.

Steady-state conductivity matches that of metallic nanoribbons.

Transient behavior aligns with uniform electric field effects in graphene.

Abstract

We theoretically investigate the time-dependent ballistic transport in metallic graphene nanoribbons after the sudden switch-on of a bias voltage $V$. The ribbon is divided in three different regions, namely two semi-infinite graphenic leads and a central part of length $L$, across which the bias drops linearly and where the current is calculated. We show that during the early transient time the system behaves like a graphene bulk under the influence of a uniform electric field $E=V/L$. In the undoped system the current does not grow linearly in time but remarkably reaches a temporary plateau with dc conductivity $\sigma_{1}=\pi e^{2}/2h$, which coincides with the minimal conductivity of two-dimensional graphene. After a time of order $L/v_{F}$ ($v_{F}$ being the Fermi velocity) the current departs from the first plateau and saturates at its final steady state value with conductivity $\sigma_{2}=2e^{2}/h$ typical of metallic nanoribbons of finite width.