Strongly anisotropic spin response as a signature of the helical regime in Rashba nanowires

Rashba nanowires in a magnetic field exhibit a helical regime when the spin-orbit momentum is close to the Fermi momentum, $k_F\approx k_{SO}$. We show that this regime is characterized by a strongly anisotropic electron-spin susceptibility, with an exponentially suppressed signal along one direction in spin space, and that there are no low-frequency spin fluctuations along this direction. Since the spin response in the gapless regime $k_F\neg \approx k_{SO}$ has a power-law behavior in all three directions, spin measurements provide a signature of the helical regime that complements spin-insensitive conductance measurements.

Figure 1

Panel (a) depicts the analyzed setup. A quantum wire with Rashba spin-orbit interaction $\sim$${\mathit{\eta }}_{\mathrm{SO}}·\mathit{S}$ is subject to a magnetic field parallel to the wire axis and perpendicular to the direction set by the spin-orbit coupling ($\mathit{S}$ denotes the electron spin). Panel (b) shows the spectrum $E\left(k\right)$ of the Rashba nanowire as a function of the momentum $k$. The magnetic field $\mathit{B}$ mixes the spin species around $k=0$ and thus opens up a gap. For large chemical potentials $\mu$, the particles close to the Fermi points at $\pm k_{+}$ and $\pm k_{-}$ with $k_{\pm }=k_F\pm k_{SO}$ have spins approximately aligned along the direction set by the spin-orbit interaction. The colors in panel (b) indicate this spin polarization (red corresponds to spin up and blue to spin down). The dotted lines show the spin-polarized bands in the absence of a magnetic field.