Smooth electron waveguides in graphene

R. R. Hartmann, N. J. Robinson, and M. E. Portnoi
Phys. Rev. B 81, 245431 – Published 23 June 2010

Abstract

We present exact analytical solutions for the zero-energy modes of two-dimensional massless Dirac fermions fully confined within a smooth one-dimensional potential V(x)=α/cosh(βx), which provides a good fit for potential profiles of existing top-gated graphene structures. We show that there is a threshold value of the characteristic potential strength α/β for which the first mode appears, in striking contrast to the nonrelativistic case. A simple relationship between the characteristic strength and the number of modes within the potential is found. An experimental setup is proposed for the observation of these modes. The proposed geometry could be utilized in future graphene-based devices with high on/off current ratios.

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  • Received 28 May 2010

DOI:https://doi.org/10.1103/PhysRevB.81.245431

©2010 American Physical Society

Authors & Affiliations

R. R. Hartmann, N. J. Robinson, and M. E. Portnoi*

  • School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom

  • *m.e.portnoi@exeter.ac.uk

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Issue

Vol. 81, Iss. 24 — 15 June 2010

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