Time-dependent transport in graphene nanoribbons

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.

5 pages, 5 figures

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