Smooth electron waveguides in graphene
Hartmann, Richard R.
Physical Review B - Condensed Matter and Materials Physics
American Physical Society
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.
Copyright © 2010 American Physical Society
Vol. 81 (24), article 245431