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

We provide a general transport theory for spin-polarized scanning tunneling microscopy (STM) through a doped topological insulator (TI) surface. It is found that different from the conventional magnetic substrate, the tunneling conductance through the tip-TI surface acquires an extra component determined by the in-plane spin texture, exclusively associated with the spin momentum locking. Importantly, this extra conductance unconventionally depends on the spatial azimuthal angle of the magnetized STM tip. By introducing a magnetic impurity to break the symmetry of rotation and local time reversal of the TI surface, we find that the measurement of the spatial resolved conductance can reconstruct the helical structure of spin texture, from which the spin-momentum locking angle can be extracted if the in-plane magnetization is induced purely by the spin-orbit coupling of surface Dirac electrons. Our theory offers an alternative way, differing from existing in-plane-current polarization probed in a multi-terminal setup or angle resolved photoemission spectroscopy, to electrically identify the helical spin texture on TI surfaces.