Signature of interaction in dc transport of ac-gated quantum spin Hall edge states

In the presence of a scattering potential, electron transport in a quantum wire is known to be dramatically modified by backward-scattering and unaffected by forward-scattering processes. We show that the scenario is quite different in quantum spin Hall edge states coupled at a constriction. The helical nature of these states leads to the appearance of a forward-scattering spin channel that is absent in other Luttinger-liquid realizations. Suitably applied ac gate voltages can thus operate on the spin of electrons tunneling across the constriction, and induce in the dc tunneling current a cusp pattern that represents the signature of the edge-state electronic interaction.

Figure 1

Helical edge states flow in a QSHE bar (circled arrows denote spin orientation). Two ac gate voltages $V_{g,T}$ and $V_{g,B}$ applied with opposite phase across a QPC affect the spin of the tunneling electrons and, in the presence of electron-electron interaction, modify the dc current.

Figure 2

The tunneling current across the QPC as a function of the dc bias voltage frequency, normalized to the value $G_{\mathrm{tun}}^0=G_{\mathrm{tun}}{|}_{\omega =0}$. The cusps at integer values of the spin gate frequency $\omega$ are a signature of electron-electron interaction (here $K=0.7$). Different curves refer to different values of the spin gate parameter: $z=1$ (black thick line), $z=3$ (red thin line), and $z=4$ (blue dashed line). Inset: For noninteracting electrons, the two nonequilibrium distributions of the electrons incoming to the QPC.