Spin-to-charge conversion on the edge of quantum spin Hall insulator

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

We present our theoretical work on dynamical spin-to-charge conversion at the edge of a quantum spin Hall insulator (QSHI), namely a two-dimensional topological insulator with helical edge states. Interconversion between spin- and charge-related quantities has been a key idea in making use of magnetic materials, especially in the context of spintronics. QSHI is a typical system showing a universal charge-to-spin conversion behavior, namely the quantum spin Hall effect, whereas the spin-to-charge conversion therein is still not clearly understood. At a lateral heterojunction of a ferromagnet (FM) and a QSHI, it has been theoretically demonstrated that magnetization dynamics induces a charge current along the edge of QSHI; however, its mechanism from the viewpoint of spin-to-charge conversion still remains to be clarified. In order to understand the spin transfer and the spin-to-charge conversion mechanism in QSHI, we investigate the many-body dynamics of the electrons under the magnetization dynamics at the QSHI-FM junction. We analytically treat the electron dynamics in terms of the Floquet-Keldysh formalism, and compare two physical quantities present on the edge: the spin injection rate from the FM into the QSHI, and the charge current induced along the edge. Whereas the edge current seen in the previous works is reproduced, we find that it is not proportional to the spin injection rate, especially when the exchange interaction at the junction is strong enough. This relation implies that the spin-to-charge conversion in this system cannot be considered as the inverse spin Hall effect, while it can be rather seen as the inverse Edelstein effect, in which an electron spin accumulation at the junction is converted to a charge current. We also focus on the energy transfer at the junction, and interpret this phenomenon in terms of magnon exchange.