Two distinct ballistic processes in graphene at Dirac point

TL;DR

This paper investigates two different ballistic transport mechanisms in graphene at the Dirac point, revealing a crossover from interband electron-hole pair creation to intraband evanescent wave conduction, depending on time scales and electric field strength.

Contribution

It identifies and characterizes two distinct ballistic transport processes in graphene, showing their dependence on time scales, electric field, and geometry, and clarifies their experimental implications.

Findings

At short times, electric fields create electron-hole pairs leading to a conductivity of pi/2 e^2/h.

At longer times, conductivity approaches 4/pi e^2/h due to evanescent modes.

Interband transitions dominate at strong electric fields beyond linear response.

Abstract

The dynamical approach is applied to ballistic transport in mesoscopic graphene samples of length L and contact potential U. At times shorter than both relevant time scales, the flight time and \hslash/U, the major effect of the electric field is to create electron - hole pairs, i.e. causing interband transitions. In linear response this leads (for width W>>L) to conductivity pi/2 e^{2}/h. On the other hand, at times lager than the two scales the mechanism and value are different. It is shown that the conductivity approaches its intraband value, equal to the one obtained within the Landauer-Butticker approach resulting from evanescent waves. It is equal to 4/pi e^{2}/h for W>>L. The interband transitions, within linear response, are unimportant in this limit. Between these extremes there is a crossover behaviour dependent on the ratio between the two time scales. At strong electric fields (beyond linear reponse) the interband process dominates. The electron-hole mechanism is universal, namely does not depend on geometry (aspect ratio, topology of boundary conditions, properties of leads), while the evanescent modes mechanism depends on all of them. On basis of the results we determine, that while in absorption measurements and in DC transport in suspended graphene the first conductivity value was measured, the latter one would appear in experiments on small ballistic graphene flakes on substrate.