Semiclassical Approach to the Physics of Smooth Superlattice Potentials in Graphene
arXiv:1301.2790 · doi:10.1103/PhysRevB.89.195435
Abstract
Due to the chiral nature of the Dirac equation, 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 example for such a system is neutral graphene with a symmetrical unidirectional SL. We show here that in smooth SLs, a semiclassical approximation provides a good mathematical description for particles. 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 two dimensional SLs in general, 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 ballistic 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.
13 pages, 9 figures, minor corrections, version published in PRB
References in corpus (19)
- The electronic properties of graphene
- Andreev reflection and Klein tunneling in graphene
- Bipolar supercurrent in graphene
- Emergence of Superlattice Dirac Points in Graphene on Hexagonal Boron Nitride
- Controlling electron-phonon interactions in graphene at ultra high carrier densities
- Dirac Cones and Minigaps for Graphene on Ir(111)
- New Generation of Massless Dirac Fermions in Graphene under External Periodic Potentials
- Josephson effect in ballistic graphene
- Electron Beam Supercollimation in Graphene Superlattices
- Electron-phonon coupling and electron self-energy in electron-doped graphene: calculation of angular resolved photoemission spectra
- Kohn-Luttinger superconductivity in graphene
- Landau Levels and Quantum Hall Effect in Graphene Superlattices
- Transport in superlattices on single layer graphene
- Evidence for Superlattice Dirac Points and Space-dependent Fermi Velocity in Corrugated Graphene Monolayer
- Superconducting States in pseudo-Landau Levels of Strained Graphene
- Superconductivity of disordered Dirac fermions
- Magnetic and Kohn-Luttinger instabilities near a Van Hove singularity: monolayer versus twisted bilayer graphene
- Effective Magnetic Fields in Graphene Superlattices
- Transport in Graphene superimposed by a moving Electrical Superlattice Potential
Cited by in corpus (4)
- Interaction-induced singular Fermi surface in a high-temperature oxypnictide superconductor
- Strain Enhanced Superconductivity in Li-Doped Graphene
- Electronic structure of graphene: (nearly) free electrons bands vs. tight-binding bands
- Fate of superconductivity in disordered Dirac and semi-Dirac semimetals