Abstract
We report a theoretical study of the quantized spin pump in a traditional quantum pump device that is based on the helical edge states of a quantum spin Hall insulator. By introducing two time-dependent magnetizations out of phase as the pumping parameters, we found that when the Fermi energy resides in the energy gap opened by magnetization, an integer number of charges or spins can be pumped out in a pumping cycle and ascribed to the possible topological interface state born in between the two pumping potentials. The quantized pump current can be fully spin-polarized, spin-unpolarized, or pure spin current while its direction can be abruptly reversed by some system parameters such as the pumping phase and local gate voltage. Our findings may shed light on generation of a quantized spin pump.
Highlights
Quantum parametric pump like the classic Archimedean screw one that can pump water by a rotating spiral tube is a striking topic in the context of quantum transport through nanostructures and arises in nature from the geometric Berry phases and quantum interference effects[1,2,3,4,5]
A celebrated proposal of quantized pump is the Thouless topological pump[17] in which a one-dimensional (1D) moving potential can pump out integral charges in a pump cycle, when the Fermi energy lies in the energy gap opened by the moving potential
Since the staggered potentials are very difficult to be operated in graphene, and the massless Dirac electrons are ubiquitous in the edge or surface states of a topological insulator, we in this work investigate the possible quantized parametric pump effect by utilizing such topological edge states, which can, in principle, be gapped by introducing some interaction breaking the symmetry that protects the original topological state
Summary
We consider typical pump devices based on the 2D QSHI as schematically shown in Fig. 1, where two ferromagnetic (FM) islands are deposited either on the whole QSHI covering two helical edge states [Fig. 1(a)] or on one boundary of QSHI [Fig. 1(b)]. It is noted here that M0 is considered to be less than the strength of spin orbit interaction, M0 < λso, because λso represents the bulk energy gap of QSHI and in our model of quantized spin pump, only the electrons in the helical edge states are assumed active in the pump process. The spin-resolved pumped current flowing into the right lead, IR, is presented, from which one can find that both current and spin directions are reversed, i.e., the charge current is conserved, Ic = IL + IR = 0, but the spin tion pcurercreesnstioisnnoonntchoensseinrgveledbIoLsu+ndIaRrsy≠of0Q(SIαHs I=40,4I1α:↑o−ne This situation is similar to flowing into the pumping the uniform region from magnetizaleft or right lead experiences a flip and flows into the opposite lead due to the limitation of the electron chirality of helical edge states
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