Topological spin pumps coupled by a magnetic impurity

¹ National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University Nanjing 210093, China
² Collaborative Innovation Center of Advanced Microstructures, Nanjing University - Nanjing 210093, China

^(a) shengli@nju.edu.cn

Received: 8 April 2016
Accepted: 17 May 2016

Abstract

The recently proposed topological spin pump is a full spin analogue to the famous Thouless charge pump, in the sense that it is protected by bulk band topology alone and independent of any symmetries. The previous works were however confined to a single one-dimensional (1D) pump with spin Chern number or a series of such pumps in parallel without any interaction. In this paper, we investigate the influence of coupling between two 1D spin Chern pumps by a magnetic impurity potential, which also breaks the time-reversal symmetry, on the spin pumping effect. By using the Green's function and Born approximation, it is shown that the leading correction to the spin pumped per cycle due to the impurity scattering is of the second order in the impurity potential. For not very strong impurity potential, the spin pumped per cycle in units of stays near the quantized value determined by the total spin Chern number of the system , for all the cases in which both, either or none of the two pumps are topologically nontrivial, corresponding to , 2 or 0, respectively. This result demonstrates that the topological spin pumps can be generally classified by different integer values of the total spin Chern number .