Finite-temperature conductance of interacting quantum wires with Rashba spin-orbit coupling

We calculate the finite-temperature conductance of clean, weakly interacting one-dimensional quantum wires subject to Rashba spin-orbit coupling and a magnetic field. For chemical potentials near the center of the Zeeman gap ($\mu =0$), two-particle scattering causes the leading deviation from the quantized conductance at finite temperatures. On the other hand, for $\left|\mu \right|>0$, three-particle scattering processes become more relevant. These deviations are a consequence of the strongly nonlinear single-particle spectrum, and are thus not accessible using Luttinger liquid theory. We discuss the observability of these predictions in current experiments on InSb nanowires and in “spiral liquids,” where a spontaneous ordering of the nuclear spins at low temperatures produces an effective Rashba coupling.

Figure 1

Single-particle spectra ${\epsilon }_{\pm }\left(k\right)$ for weak magnetic fields (${\widehat{\epsilon }}_R\gg 1$). The color coding and the arrows show the rotation of the spin quantization axis as a function of momentum. The chemical potential is in the Zeeman gap, $\left|\mu \right|<B_z$.

Figure 2

Linear conductance of a noninteracting Rashba wire for chemical potential $\mu =0$ as a function of temperature $T$ and magnetic field $B_z$.

Figure 3

Two-particle scattering process for $\mu \approx 0$. This process contributes to the conductance correction because it changes the numbers of right and left movers.

Figure 4

Three-particle scattering process for $\left|\mu \right|<B_z$. This process contributes to the conductance correction because it changes the numbers of right and left movers.