Current transfer torque and Hall conductance at the ferromagnetic topological insulators junction

In-plane magnetization on the surface of three-dimensional topological insulators (3D TIs) tunes the Dirac cone's location in thek-space. We theoretically show that a normal/ferromagnetic junction on the surface of 3D TIs bends the propagation direction of Dirac fermions when the magnetization has a component perpendicular to the junction. This effect leads to a Hall conductance, which flows parallel to the interface. Also, it creates an indirect gap that manifests itself in the longitudinal conductance of the junction. The sign of Hall conductance is related to the in-plane magnetization direction. Based on this effect, we propose a set up to detect it experimentally. Moreover, this bending effect imposes a torque on the junction calledcurrent transfer torque(CTT). We show thez-component of CTT is non-zero in the presence of bending effect. Also, its value and direction that can be used in fabricating new devices are related to the Hall conductance.