Unidirectional Seebeck effect in magnetic topological insulators

We theoretically investigate the temperature gradient-dependent or unidirectional Seebeck effect (USE) in a magnetic/ nonmagnetic topological insulator (TI) heterostructure with in-plane magnetization in terms of the semiclassical electron dynamics and Fermi golden rule. The USE has a quantum origin arising from the magnon asymmetric scattering of surface Dirac electrons on TI. We discuss the USE in the heterostructures, Cr$_{x}$(Bi$_{1-y}$Sb$_y$)$_{2-x}$Te$_{3}$/ (Bi$_{1-y}$Sb$_{y})_2$Te$_{3}$. The USE exhibits $\cos\phi$-dependence (measured from $y$-direction) on the orientation of magnetization. It's found that the sign of USE stays unchanged when the system is transferred from $p$-doping to $n$-doping. The USE shows on inverse-linearly temperature dependent at high temperature.