Fractal butterflies in buckled graphenelike materials

Abstract

We study theoretically the properties of buckled graphene-like materials, such as silicene and germanene, in a strong perpendicular magnetic field and a periodic potential. We analyze how the spin-orbit interaction and the perpendicular electric field influences the energy spectra of these systems. When the magnetic flux through a unit cell of the periodic potential measured in magnetic flux quantum is a rational number, α = p/q, then in each Landau level the energy spectra have a band structure, which is characterized by the corresponding gaps. We study the dependence of those gaps on the parameters of the buckled graphene-like materials. Although some gaps have weak dependence on the magnitude of the spin-orbit coupling and the external electric field, there are gaps that show strong nonomonotic dependence on these parameters. For α = 1/2, the spin-orbit interaction also opens up a gap at one of the Landau levels. The magnitude of the gap increases with spin-orbit coupling and decreases with the applied electric field.

Self-similar transport, spin polarization and thermoelectricity in complex silicene structures

“…Electric, magnetic and optical fields as well as doping can induce phases like valley-polarized metal, quantum anomalous Hall effect, quantum spin Hall effect and chiral topological superconductivity. Furthermore, silicene exhibits a highly fragmented energy spectrum with fractal characteristics (Hofstadter butterfly) under strong perpendicular magnetic field and a periodic potential 34 . The fractal patterns depend on the SOC as well as the external perpendicular electric field.…”

Comments on the fractal energy spectrum of honeycomb lattice with defects

“…This intriguing behavior of Bloch electrons has long attracted the major interest of researchers from various perspectives. In a two-dimensional system, the Hofstadter problem is addressed for various choice of lattices: general Bravais lattice [5], buckled graphene like materials [6] and square lattice with next-nearest-neighbor hopping [7]. More recently Hofstadter's butterfly appears in relation to the quantum geometry [8,9] and it is also surveyed from a perspective of mathematical physics [10][11][12].…”

Hydrodynamic simulations of terahertz oscillation in double-layer graphene

“…The discovery of graphene opened a new era in material science since 2004 [1] . Graphene consists of just a single layer of carbon atoms arranged in a hexagonal lattice, which is the first truly two-dimensional (2D) crystal.…”