Transport and STM studies of hyperbolic surface states of topological insulators

Abstract

Motivated by the transmission of topological surface states through atomic scale steps, we study the transport of gapless Dirac fermions on hyperbolic surfaces. We confirm that, independent of the curvature of the hyperbolae and the sharpness of the corners, no backward scattering takes place and transmission of the topological surface states is completely independent of the geometrical shape (within the hyperbolic model) of the surface. The density of states of the electrons, however, shows a dip at concave step edges which can be measured by an STM tip. We also show that the tunneling conductance measured by a polarized scanning tunneling probe exhibits an unconventional dependence on the polar and azimuthal angles of the magnetization of the tip as a function of the curvature of the surface and the sharpness of the edge.

Edge states of a three-dimensional topological insulator

“…We have chosen k y > 0 and b x < 0 so that the states appears near the corner at (20,20) where the analysis around Eqs. (43)(44)(45)(46)(47)(48) is applicable. In accordance with the statement made after Eq.…”

“…Junctions of different surfaces of TIs (which are sometimes separated by a geometrical step or a magnetic domain wall) [24][25][26][27][28][29][30][31][32], polyhedral surfaces [33], and junctions of surfaces of a TI with normal metals or magnetic materials [34] or superconductors [35,36] have also been studied. Effects of finite sizes [37][38][39][40][41][42][43] and different orientations [31,32,[44][45][46][47][48] on the surface states have been studied. Zero energy states at the edges of a thin strip have been studied in [49] and it has been shown that these remain robust in the presence of Zeeman coupling to a magnetic field.…”

Probing surface states exposed by crystal terminations at arbitrary orientations of three-dimensional topological insulators

“…The spin textures of the surface states of TIs have been studied by spin-resolved angle resolved photoemission spectroscopy (ARPES) 12,[15][16][17] or by scanning tunneling microscope (STM) [18][19][20][21][22] via study of quasi-particle interference patterns induced by weak disorder potential. Though spinresolved ARPES serves as a very efficient probe for scanning the surface state spectrum of 3D TI leading to a complete reconstruction of the spin texture of the Fermi surface, it does not provide information regarding influence of spinmomentum locking in electrical transport properties of the surface state.…”

Spin-polarized tunneling into helical edge states: Asymmetry and conductances

“…There is experimental evidence [12] and a theoretical explanation [13] that the electron injection even into usual TLL may be characterized by charge fractionalization resulting in the currents imbalance. For helical TLL probing by the tip was considered theoretically in papers [14][15][16][17][18][19]. Experimentally it was confirmed that the TI edge state is a quantum spin Hall state [20], the helical behavior of the edge state was observed in [21], the STM experiments were reported in [22,23].…”