Smooth electron waveguides in graphene

Details Smooth electron waveguides in graphene Smooth electron waveguides in graphene

2009-08-05

arxiv.org/abs/0908.0561v3

Phys. Rev. B 81, 245431 (2010)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

8 Pages including 4 figures, an appendix and two additional figures added, references updated

Scientific paper

10.1103/PhysRevB.81.245431

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)= - {\alpha}/cosh({\beta}x), 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 {\alpha}/{\beta} for which the first mode appears, in striking contrast to the non-relativistic 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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