Backscattering between helical edge states via dynamic nuclear polarization

We show that the nonequilibrium spin polarization of one-dimensional helical edge states at the boundary of a two-dimensional topological insulator can dynamically induce a polarization of nuclei via the hyperfine interaction. When combined with a spatially inhomogeneous Rashba coupling, the steady-state polarization of the nuclei produces backscattering between the topologically protected edge states leading to a reduction in the conductance which persists to zero temperature. We study these effects in both short and long edges, uncovering deviations from Ohmic transport at finite temperature and a current noise spectrum which may hold the fingerprints for experimental verification of the backscattering mechanism.

Figure 1

Quantum spin Hall edge states dynamically polarize nuclear spins via a hyperfine interaction. Although the nonequilibrium edge states governed by chemical potentials ${\mu }_L$ and ${\mu }_R$ are drawn as sharp lines, their wave functions may overlap a large number of nuclei. Only one edge is shown, but there is an equivalent and independent transport channel at the opposite edge, where the spin polarizations are reversed.

Figure 2

An outline of sequential scattering processes for the helical edge states. It is assumed that the nuclei are unpolarized $(\langle I\rangle =0)$ in the leads but are dynamically polarized $(\langle I\rangle \ne 0)$ between them in a region with potential disorder giving rise to random Rashba scattering.

Figure 3

The induced dynamic nuclear polarization $\langle I\rangle \left(x\right)$ computed from Eq. (10) for a long $(L/{\ell }_0\gg 1)$ edge. The inset shows the dimensionless temperature profile generated via Joule heating.

Figure 4

The Fano factor calculated from the current noise in Eq. (17) is found to be parametrized by the finite size scaling form $F=1.219\left(2\right)-2.03\left(3\right){({\ell }_0/L)}^{0.65\left(3\right)}$.