  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.

Mesoscale and Nanoscale Physics