Dissipative spin pumping in two-dimensional quantum spin Hall insulator

Araki, Yasufumi   ; Misawa, Takahiro*; Nomura, Kentaro*

We present our theoretical work on spin pumping into a two-dimensional (2D) quantum spin Hall inslator (QSHI). Recent theories and experiments have demonstrated the QSHI phase in a monolayer of transition metal dichalcogenide 1T'-WTe2, which can be easily engineered in contrast to traditionally-known HgTe/CdTe and InAs/GaSb quantum wells. While the theory of spin pumping is well established in normal metals by focusing on the spin-dependent electron scattering at the interface, it is unreliable for topologically nontrivial interfaces in such systems. In the present work, we consider a junction of a ferromagnet and a 2D QSHI at its 1D edge, and demonstrate the pumping of angular momentum from the spin-precessing ferromagnet into the QSHI. Using the Floquet theory for the electrons on the helical edge states, we analytically show that the time-periodic precession of the magnetization drives a charge current on the edge, for the whole range of precession frequency. This edge current can be regarded as a consequence of the inverse spin Hall effect intrinsic to the QSHI, which converts the injected spin current into a transverse charge current. By varying the precession frequency of the magnetization and the coupling strength at the junction, we find a clear crossover between two regimes: the adiabatic regime, where the slow magnetization precession drives a quantized pumping, and the resonant regime, where the fast precession leads to a suppressed pumping. We also incorporate the effect of orbital dependence in the exchange coupling at the edge, and show numerically that it shifts the crossover point between the adiabatic and resonant regimes.