Transport and STM studies of hyperbolic surface states of topological insulators

TL;DR

This study investigates how topological surface states in insulators transmit across hyperbolic surfaces, revealing shape-independent transmission and unique tunneling conductance behaviors influenced by surface curvature and magnetization angles.

Contribution

It demonstrates that topological surface states are unaffected by surface curvature or sharpness, and explores their tunneling conductance dependence on magnetization orientation.

Findings

No backward scattering occurs regardless of surface shape.

Density of states dips at concave step edges detectable by STM.

Tunneling conductance varies with magnetization angles and surface curvature.

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.