Inverse quantum spin Hall effect generated by spin pumping from precessing magnetization into a graphene-based two-dimensional topological insulator

Abstract

We present a multiterminal nanostructure for electrical probing of the quantum spin Hall effect (QSHE) in two-dimensional (2D) topological insulators (TIs). The device consists of a ferromagnetic (FM) island with precessing magnetization that pumps (in the absence of any bias voltage) pure spin current symmetrically into the left and right adjacent 2D TIs modeled as graphene nanoribbons with the intrinsic spin-orbit (SO) coupling. In the reference frame rotating with magnetization, the device is mapped onto a dc circuit with twice as many terminals whose effectively half-metallic ferromagnetic electrodes are biased by the frequency $\ensuremath{\hbar}\ensuremath{\omega}/e$ of the microwave radiation driving the magnetization precession at the ferromagnetic resonance conditions. The QSH regime of the six-terminal $\text{TI}|\text{FM}|\text{TI}$ nanodevice, attached to two longitudinal and four transverse normal metal electrodes, is characterized by the SO-coupling-induced energy gap, chiral spin-filtered edge states within finite length TI regions, and quantized spin Hall conductance when longitudinal bias voltage is applied, despite the presence of the FM island. The same unbiased device, but with precessing magnetization of the central FM island, blocks completely pumping of total spin and charge currents into the longitudinal electrodes while generating dc transverse charge Hall currents. Although these transverse charge currents are not quantized, their induction together with zero longitudinal charge current is a unique electrical response of TIs to pumped pure spin current that cannot be mimicked by SO coupled but topologically trivial systems. In the corresponding two-terminal inhomogeneous $\text{TI}|\text{FM}|\text{TI}$ nanostructures, we image spatial profiles of local spin and charge currents within TIs which illustrate transport confined to chiral spin-filtered edges states while revealing concomitantly the existence of interfacial spin and charge currents flowing around $\text{TI}\ensuremath{\mid}\text{FM}$ interfaces and penetrating into the bulk of TIs over some short distance.