Abstract
We develop an analytical theory of the low-frequency ac quantum spin Hall (QSH) effect based upon the scattering matrix formalism. It is shown that the ac QSH effect can be interpreted as a bulk quantum pumping effect. When the electron spin is conserved, the integer-quantized ac spin Hall conductivity can be linked to the winding numbers of the reflection matrices in the electrodes, which also equal to the bulk spin Chern numbers of the QSH material. Furthermore, a possible experimental scheme by using ferromagnetic metals as electrodes is proposed to detect the topological ac spin current by electrical means.
Highlights
Topological insulators (TIs) are currently on the research front of condensed matter physics, because of their fundamental interest and potential applications in spintronic devices[1,2,3,4,5,6,7,8,9,10,11,12,13]
We show that the basic characteristics of the low-frequency ac quantum spin Hall (QSH) effect can be interpreted in terms of single-parameter adiabatic spin pumping
We focus on the adiabatic pumping regime, where the frequency ω of the ac electric field is much smaller than the bulk energy gap Δgap of the QSH material[27]
Summary
When the electron spin is conserved, the integer-quantized ac spin Hall conductivity can be linked to the winding numbers of the reflection matrices in the electrodes, which equal to the bulk spin Chern numbers of the QSH material. A possible experimental scheme by using ferromagnetic metals as electrodes is proposed to detect the topological ac spin current by electrical means. The time dependence in the driving electric field is essential for generating ac spin current flowing from the bulk of the QSH sample to an electrode. By using the well-established time-dependent scattering matrix formalism, the ac spin Hall conductivity is linked to the winding numbers of the reflection matrices in the electrode, which equal to the spin Chern numbers of the QSH material. Spin current will induce an electrical voltage difference along the electrodes, suggesting a possible experimental way to observe the ac QSH effect by electrical means
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