Generation of Multiple Dirac Cones in Graphene under Double-periodic and Quasiperiodic Potentials
arXiv:1306.0297 · doi:10.7566/JPSJ.82.113706
Abstract
We investigate generation of new Dirac cones in graphene under double-periodic and quasiperiodic superlattice potentials. We first show that double-periodic potentials generate the Dirac cones sporadically, following the Diophantine equation, in spite of the fact that double-periodic potentials are also periodic ones, for which previous studies predict consecutive appearance of the cones. The sporadic appearance is due to the fact that the dispersion relation of graphene is linear only up to an energy cutoff. We then show that quasiperiodic potentials generate the new Dirac cones densely with its density depending on the energy. We also extend the above predictions to other materials of Dirac electrons with different energy cutoffs of the linear dispersion.
4 pages, 5 figures
References in corpus (12)
- Electric Field Effect in Atomically Thin Carbon Films
- The electronic properties of graphene
- The structure of suspended graphene sheets
- A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
- Emergence of Superlattice Dirac Points in Graphene on Hexagonal Boron Nitride
- Anisotropic behaviors of massless Dirac fermions in graphene under periodic potential
- Dirac Cones and Minigaps for Graphene on Ir(111)
- New Generation of Massless Dirac Fermions in Graphene under External Periodic Potentials
- Transport in Bilayer Graphene: Calculations within a self-consistent Born approximation
- Quasi-Periodic Nanoripples in Graphene Grown by Chemical Vapor Deposition and Its Impact on Charge Transport
- Electronic band gap and transport in Fibonacci quasi-periodic graphene superlattice
- Multifractal Wave Functions of a System with a Monofractal Energy Spectrum