Generation of Multiple Dirac Cones in Graphene under Double-periodic and Quasiperiodic Potentials

TL;DR

This paper explores how double-periodic and quasiperiodic potentials induce new Dirac cones in graphene, revealing sporadic and dense generation patterns influenced by energy cutoffs and extending findings to other Dirac materials.

Contribution

It demonstrates that double-periodic potentials produce Dirac cones sporadically following a Diophantine equation, and quasiperiodic potentials generate them densely, extending the understanding of Dirac cone generation mechanisms.

Findings

Double-periodic potentials generate Dirac cones sporadically according to a Diophantine equation.

Quasiperiodic potentials produce a dense distribution of new Dirac cones.

Results extend to other Dirac materials with different energy cutoffs.

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.