Electrically controlled pumping of spin currents in topological insulators

Pure spin currents are shown to be generated by an electrically controlled quantum pump applied at the edges of a topological insulator. The electric rather than the more conventional magnetic control offers several advantages and avoids, in particular, the necessity of delicate control of magnetization dynamics over tiny regions. The pump is implemented by pinching the sample at two quantum point contacts and phase modulating two external gate voltages between them. The spin current is generated for the full range of parameters. On the other hand, pumping via amplitude modulation of the interboundary couplings generates both charge and spin currents, with a pure charge current appearing only for special values of the parameters for which the Aharonov-Bohm flux takes integer values. Our setup can therefore serve to fingerprint the helical nature of the edges states with the zeros of the pumped spin and charge currents occurring at distinct universal locations where the Fabry-Pérot or the Aharonov-Bohm phases take integer values.