Landau levels and magnetic oscillations in gapped Dirac materials with intrinsic Rashba interaction

Abstract

A new family of the low-buckled Dirac materials which includes silicene, germanene, etc. is expected to possess a more complicated sequence of Landau levels than in pristine graphene. Their energies depend, among other factors, on the strength of the intrinsic spin-orbit (SO) and Rashba SO couplings and can be tuned by an applied electric field E z . We studied the influence of the intrinsic Rashba SO term on the energies of Landau levels using both analytical and numerical methods. The quantum magnetic oscillations of the density of states are also investigated. A specific feature of the oscillations is the presence of the beats with the frequency proportional to the field E z . The frequency of the beats becomes also dependent on the carrier concentration when Rashba interaction is present allowing experimental determination of its strength.

Landau levels in spin-orbit coupling proximitized graphene: Bulk states

“…This is due to the downfolding procedure, which neglects higher order terms. Equations (23) and (24) are plotted in Fig. 5.…”

“…Thus, we can combine Eqs. (23) and (24) to estimate the critical magnetic field for which we expect the inner states to cross. Inserting model values for WSe 2 , we obtain a critical field of 1.8 mT.…”

“…The physics of symmetry-broken honeycomb lattices has been extensively studied theoretically [20][21][22][23][24]. However, the interplay between orbital magnetic fields and proximity SOC is a relatively recent subject; see, for example, Ref.…”

“…When symmetries in a hexagonal lattice become broken as in, e.g., buckled silicene, the fourfold Landau level degeneracy is lifted [23] and gaps can be introduced. While spin-orbit coupling proximitized graphene has many similarities to silicene, in proximitized graphene intrinsic SOC is sublattice resolved and Rashba SOC is momentum independent [4,21,24]. The interplay of uniform intrinsic and Rashba SOC with orbital magnetic fields was studied in Refs.…”

Magnetic properties of Dirac fermions in a buckled honeycomb lattice

“…For µ above both gaps [µ 3 in Fig. 10(c)], there are two frequencies, and interference will be observed 27,28,58 . When the difference between A min (µ), and A max (µ) is small, a strong beating is present.…”