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Dissipative spin pumping into two-dimensional quantum spin Hall insulator

2次元量子スピンホール絶縁体における散逸的スピンポンピング

荒木 康史; 三澤 貴宏*; 野村 健太郎*

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

The two-dimensional quantum spin Hall insulator (2D QSHI) is the most primitive but quite important realization of topological insulator. It shows the helical edge states protected by time-reversal symmetry, whereas the quantized spin Hall conductivity in the bulk. In the present work, we theoretically investigate the spin pumping from a precessing ferromagnet into a 2D QSHI thoroughly from the adiabatic to nonadiabatic regimes, both analytically and numerically. We analytically treat the dynamics of the edge-state electrons coupled to the precessing ferromagnet by the Floquet theory, and derive the pumped current as a function of the exchange energy and the precession frequency. We find that a heat bath for the edge electrons governs the transition between the adiabatic and nonadiabatic regime: when the edge electrons are coupled with a heat bath, their spin and energy can dissipate into the bath by a certain rate, eventually reaching a periodic steady state. The pumped current on the becomes quantized when the exchange energy exceeds the dissipation rate. We also calculate the edge current numerically on the 2D lattice model, and find that the bulk states in the QSHI effectively serves as the heat bath for the edge electrons.

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