Protected edge states in silicene antidots and dots in magnetic field

Abstract

Silicene systems, due to the buckled structure of the lattice, manifest remarkable intrinsic spinorbit interaction triggering a topological phase transition in the low-energy regime. Thus, we found that protected edge states are present in silicene antidots and dots, being polarized in valley-spin pairs. We have also studied the effect of the lattice termination on the properties of the single electron energy levels and electron density distribution of silicene antidots and dots situated in a perpendicular magnetic field. Our calculations confirmed that the topological edge states are propagating over the perimeter of the antidot/dot for both ideal or realistic edge termination containing roughness on the atomic length scale. The valley polarization and the slope of the energy line as a function of the magnetic field is, however, reduced when the antidot or dot has a rough edge.

Resonant electron scattering by a graphene antidot

“…For negatively (positively) charged antidot these peaks shift to the left (right), when the absolute value of charge increases, in agreement with the renormalization of ESs spectrum discussed above. The width of the peaks determined by the imaginary part of the energy is also in qualitative agreement with (25): at negative q the imaginary part of the energy decreases when |q| increases and the peaks become narrower, which corresponds to more stationary states; at positive q, the imaginary part of the energy increases when |q| increases, and the peaks become wider. One way to detect these resonanses is to measure the conductivity of graphene sample with an array of identical nanoholes, another one is to measure the LDOS near an antidot.…”

“…The resonant scattering of graphene electrons occurs when its energy coincides with the edge Dependence of the transport cross section σtr on energy for the scattering by positively (upper panel, q > 0) and negatively (lower panel, q < 0) charged antidot and a = −0.15. When |q| increases, the resonant peaks, which position is determined by the ESs spectrum, shift to the right for positively charged antidot, and to the left if charge is negative in agreement with Eqs (25,26)…”

Band inversion at critical magnetic fields in a silicene quantum dot

“…We have performed our calculations in the continuous model, which is a long-wave approximation of the more fundamental tight binding model. Therefore, we have disregarded the effect of lattice termination on the energy spectrum [18]. Nevertheless, we hope that the effect of the boundary irregularities on the spectrum is negligible when the radius R is much larger than the lattice constant, and our results on band inversion at critical magnetic fields remain valid at least in this regime.…”

“…Of course, a more detailed calculation inside the tight binding framework with more realistic edge termination, like the one done in Ref. [18] for silicene in magnetic field, is necessary to account for the robustness of the band inversion phenomenon. We think that this question deserves a separate study and will be considered elsewhere.…”

Transport through graphenelike flakes with intrinsic spin-orbit interactions

“…This problem in the absence of spinorbit interaction was considered, e.g., in Refs. [18,30,31], from which it follows that localized edge magnetic moments exist mainly on zigzaglike fragments of an arbitrary boundary. To address this issue in the presence of spin-orbit interaction in the Appendix we consider a flake of circular shape exhibiting some irregularities.…”