Gap formation in helical edge states with magnetic impurities

Abstract

Helical edge states appear at the surface of two dimensional topological insulators and are characterized by spin up traveling in one direction and the spin down traveling in the opposite direction. Such states are protected by time reversal symmetry and no backscattering due to scalar impurities can occur. However, magnetic impurities break time reversal symmetry and lead to backscattering. Often their presence is unintentional, but in some cases they are introduced into the sample to open up gaps in the spectrum. We investigate the influence of random impurities on helical edge states, specifically how the gap behaves in the realistic case of impurities having both a magnetic and a scalar component. It turns out that for a fixed magnetic contribution the gap closes when either the scalar component, or Fermi velocity is increased. We compare diagrammatic techniques in the self-consistent Born approximation to numerical calculations which yields good agreement. For experimentally relevant parameters we find that even moderate scalar components can be quite detrimental for the gap formation.

Doping-controlled surface conduction in topological insulators with warping effects

“…One way to examine the topological stability is to probe the energy spectrum of topological insulators in the presence of randomly distributed ionized and magnetized impurities. The conducting surface states of these materials are robust against the effect of non-magnetic disorder, while the Dirac surface state spectrum can be gapped by magnetic impurities or other perturbations breaking timereversal symmetry [16][17][18][19][20][21][22][23]. Nevertheless, a well-defined band-gap is not always formed by magnetic impurities, as observed in some experiments [24][25][26].…”

“…The difference between t-matrix approximation and self-consistent t-matrix approximation is that the former uses the unperturbed Green's function, while in the latter the impurity averaged Green's function is used in the t-matrix expansion. In the self-consistent t-matrix approximation, the t-matrix expansion is given by [20,39,40]…”

“…The continuum surface model and also a threedimensional tight-binding lattice model, showed that the energy gap induced by ferromagnetically aligned magnetic impurities on the surface of a topological insulator can be filled, due to the scattering off the nonmagnetic potential of the impurities that induce low-energy impurity resonances [19]. The influence of random impurities on helical edge states for a fixed magnetic contribution has been studied [20]. It was shown that the gap is filled when either the scalar potential or Fermi velocity is in-creased [20].…”

“…The influence of random impurities on helical edge states for a fixed magnetic contribution has been studied [20]. It was shown that the gap is filled when either the scalar potential or Fermi velocity is in-creased [20]. Based on kernel polynomial expansion and Green's function approaches, the local density of states, single-particle spectral function, and electric conductance on the surface of 3D topological insulators have been investigated [21].…”

Conduction of surface electrons in a topological insulator with spatially random magnetization

“…For instance, it was shown that the presence of magnetic impurities at the surface of TIs may lead to the in-plane magnetoresistance which is a mixture of the anisotropic and spin magnetoresistance, as well as to planar Hall effect 29 . Moreover, random magnetic impurities may lead to opening an energy gap for the edge states [30][31][32] , and also may improve quality of the quantum anomalous Hall effect in magnetic TIs 33 . Recently the electron states at the surface of a TI attached to a ferromagnet, described by the XY model, have also been considered, and it was shown that the classical magnetic fluctuations in the ferromagnet could be mapped onto the problem of Dirac fermions in the random magnetic field 34 .…”