1301.2790 (Juergen Dietel et al.)

Semiclassical Approach to the Physics of Smooth Superlattice Potentials
in Graphene    [PDF]

Juergen Dietel, Hagen Kleinert

Due the chiral nature of the Dirac equation, that governs the electron dynamics in graphene, the overlying of an electrical superlattice (SL) can open new Dirac points on the Fermi-surface of the energy spectrum. These lead to novel low-excitation physical phenomena. A typical such system is neutral graphene with a symmetrical unidirectional SL. We show here that in smooth SLs, a good mathematical description for particles can be achieved by the semiclassical approximation. Due to the one-dimensional nature of the unidirectional potential, a wavefunction description leads to a generalized Bohr-Sommerfeld quantization condition for the energy eigenvalues. In order to pave the way for the application of semiclassical methods to general two dimensional SLs, we compare these energy eigenvalues with those obtained from numerical calculations, and with the results from a semiclassical Gutzwiller trace formula via the beam-splitting technique. Finally, we calculate conductivities in general point-symmetric unidirectional SLs with one electron and one hole region in the fundamental cell showing only Klein scattering of the semiclassical wavefunctions.

View original: http://arxiv.org/abs/1301.2790