  We propose a multiterminal nanostructure for electrical probing of the
quantum spin Hall effect (QSHE) in two-dimensional (2D) topological insulators.
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. The QSH regime of the
six-terminal TI|FM|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 TI|FM|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 TI|FM interfaces and penetrating into the bulk
of TIs over some short distance.
