# Transport theory for electrical detection of the spin texture and spin-momentum locking of topological surface states

## TL;DR

This paper develops a theoretical framework for electrically detecting the helical spin texture of topological insulator surface states using spin-polarized STM, revealing how conductance depends on spin-momentum locking and magnetization orientation.

## Contribution

It introduces a novel theory linking tunneling conductance to spin texture, enabling electrical detection of spin-momentum locking in topological insulators.

## Key findings

- Conductance depends on in-plane spin texture and azimuthal angle.
- Magnetic doping allows reconstruction of the spin texture.
- The SML angle can be extracted from conductance measurements.

## Abstract

The surface states of three-dimensional topological insulators exhibit a helical spin texture with spin locked to momentum. To date, however, the direct all-electrical detection of the helical spin texture has remained elusive owing to the lack of necessary spin-sensitive measurements. We here provide a general theory for spin polarized transports of helical Dirac electrons through spin-polarized scanning tunneling microscopy (STM). It is found that different from conventional magnetic materials, the tunneling conductance through the TI surface acquires an extra component determined by the in-plane spin texture, exclusively associated with spin momentum locking. Importantly, this extra conductance unconventionally depends on the spatial azimuthal angle of the magnetized STM tip, which is never carried out in previous STM theory. By magnetically doping to break the symmetry of rotation and time reversal of the TI surface, we find that the measurement of the spatial resolved conductance can reconstruct the helical structure of spin texture. Furthermore, one can extract the SML angle if the in-plane magnetization is induced purely by the spin-orbit coupling of surface Dirac elections. Our theory offers an alternative way, rather than using angle resolved photoemission spectroscopy, to electrical identify the helical spin texture on TI surfaces.