Influence of the Fermi velocity on the transport properties of the 3D topological insulators

Abstract

We explore the transport of the surface states quasielectrons in the 3D topological insulators through the barriers of various origin: the Fermi velocity and the electrostatic barriers. These barriers are believed to be the rectangular and one-dimensional ones. The transmission coefficient T as the function of the quasiparticle energy E and an angle of incidence θ (transmission spectra) is evaluated with the help of the effective Hamiltonian; the conductivity G is calculated on the base of the Landauer–Buttiker formula. It is shown that the value of T and G significantly depends on the ratio of the Fermi velocities in the barrier and out-of-barrier regions α = vF2/vF1. The dependence of these quantities on the strength of the electrostatic potential is analyzed. We find in particular that the effect of supertunneling manifests itself in the considered structure—being markedly dependent on the value of α. The formula which points out the energy value for which the effect of supertunneling takes place, for different α, is presented. For normal angle of the particle incidence, there is the effect analogous to the Klein paradox. The spectra T(E,θ) and G(E) substantially depend on the interplay of α, energy E and the magnitude of the electrostatic potential. Hence, by changing the problem parameters one can flexibly vary the spectra of T(E,θ) and G(E) in wide limits. The obtained results may be useful for the nanoelectronics based on the topological insulators.

Volt-ampere characteristic of the superconductive nanostructure with the andreev reflection induced by the Majorana fermiones

“…It is known that by changing this value, the spectra T (E) can be changed in a wide range, in particular in graphene. Therefore, considerable attention was paid to the study of experimental possibilities for obtaining and proposals of using in practice a spatially dependent value of vf (Wang, Liu & Wang, 2013;Concha, Tešanović, 2010;Korol, 2019;Korol & Medvid, 2019). Since Majorana modes can be observed in contact structures with graphene, priority in this paper should be given to the analysis of the dependence of the spectra on the vf.…”