Two distinct ballistic processes in graphene at the Dirac point

M. Lewkowicz, B. Rosenstein, and D. Nghiem
Phys. Rev. B 84, 115419 – Published 15 September 2011

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 tL=L/vg (vg is Fermi velocity) and tU=/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 WL) to conductivity σ2=π/2 e2/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-Bütticker approach resulting from evanescent waves. It is equal to σ1=4/π e2/h for WL and tUtL. The interband transitions, within linear response, are unimportant in this limit. Between these extremes there is a crossover behavior dependent on the ratio between the two time scales tL/tU. At strong electric fields (beyond linear response) 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 σ2 was measured, σ1 would appear in experiments on small ballistic graphene flakes on substrate.

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  • Received 7 July 2011

DOI:https://doi.org/10.1103/PhysRevB.84.115419

©2011 American Physical Society

Authors & Affiliations

M. Lewkowicz1, B. Rosenstein2,3,1,*, and D. Nghiem2

  • 1Physics Department, Ariel University Center of Samaria, Ariel 40700, Israel
  • 2Electrophysics Department, National Chiao Tung University, Hsinchu 30050, Taiwan, Republic of China
  • 3National Center for Theoretical Sciences, Hsinchu 30043, Taiwan, Republic of China

  • *vortexbar@yahoo.com

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Vol. 84, Iss. 11 — 15 September 2011

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