We investigate the consequences of applying electric fields perpendicularly to thin films of topological semimetals. In particular, we consider Weyl and Dirac semimetals in a configuration such that their surface Fermi arcs lie on opposite edges of the films. We develop an analytical approach based on perturbation theory and a single-surface approximation and we compare our analytical results with numerical calculations. The effect of the electric field on the dispersion is twofold: it shifts the dispersion relation and renormalizes the Fermi velocity, which would, in turn, have direct effects on quantum transport measurements. Additionally, it modifies the spatial decay properties of surface states which will impact the connection of the Fermi arcs in opposite sides of a narrow thin film.
We theoretically address the impact of a random distribution of non-magnetic impurities on the electron states formed at the surface of a topological insulator. The interaction of electrons with the impurities is accounted for by a separable pseudo-potential method that allows us to obtain closed expressions for the density of states. Spectral properties of surface states are assessed by means of the Green’s function averaged over disorder realisations. For comparison purposes, the configurationally averaged Green’s function is calculated by means of two different self-consistent methods, namely the self-consistent Born approximation (SCBA) and the coherent potential approximation (CPA). The latter is often regarded as the best single-site theory for the study of the spectral properties of disordered systems. However, although a large number of works employ the SCBA for the analysis of many-impurity scattering on the surface of a topological insulator, CPA studies of the same problem are scarce in the literature. In this work, we find that the SCBA overestimates the impact of the random distribution of impurities on the spectral properties of surface states compared to the CPA predictions. The difference is more pronounced when increasing the magnitude of the disorder.
Topologically protected surface states in semi-infinite SnTe are robust against Sb doping and preserve their spin texture, whereas in slabs they show a gap. These states are studied using first-principles and continuum model calculations.
We study the effect of the Rashba spin–orbit coupling on the Fermi arcs of topological Dirac semimetals. The Rashba coupling is induced by breaking the inversion symmetry at the surface. Remarkably, this coupling could be enhanced by the interaction with the substrate and controlled by an external electric field. We study analytically and numerically the rotation of the spin of the surface states as a function of the electron’s momentum and the coupling strength. Furthermore, a detailed analysis of the spin-dependent two-terminal conductance is presented in the clean limit and with the addition of a random distribution of impurities. Depending on the magnitude of the quadratic terms in the Hamiltonian, the spin-flip conductance may become dominant, thus showing the potential of the system for spintronic applications, since the effect is robust even in the presence of disorder.
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