We provide a theory for the tunneling conductance $G\left(V\right)$ of Dirac electrons on the surface of a topological insulator as measured by a spin-polarized scanning tunneling microscope tip for low-bias voltages $V$. We show that if the in-plane rotational symmetry on the surface of the topological insulator is broken by an external field that does not couple to spin directly (such as an in-plane electric field), $G\left(V\right)$ exhibits an unconventional dependence on the direction of the magnetization of the tip, i.e., it acquires a dependence on the azimuthal angle of the magnetization of the tip. We also show that $G\left(V\right)$ can be used to measure the magnitude of the local out-of-plane spin orientation of the Dirac electrons on the surface. We explain the role of the Dirac electrons in this unconventional behavior and suggest experiments to test our theory.

• Received 9 May 2011

DOI:https://doi.org/10.1103/PhysRevB.84.165439