Spin-orbit coupling and transport in strongly correlated two-dimensional systems

Measuring the magnetoresistance (MR) of ultraclean GaAs two-dimensional holes for a large $r_s$ range of 20–50, two striking behaviors in relation to the spin-orbit coupling (SOC) emerge in response to strong electron-electron interaction. First, in exact correspondence to the zero-field metal-to-insulator transition (MIT), the sign of the MR switches from being positive in the metallic regime to being negative in the insulating regime when the carrier density crosses the critical density $p_c$ of MIT ($r_s\sim 39$). Second, as the SOC-driven correction $\mathrm{\Delta }\rho$ to the MR decreases with reducing carrier density (or the in-plane wave vector), it exhibits an upturn in the close proximity just above $p_c$ where $r_s$ is beyond 30, indicating a substantially enhanced SOC effect. This peculiar behavior echoes with a trend of delocalization long suspected for the SOC-interaction interplay. Meanwhile, for $p<p_c$ or $r_s>40$, in contrast to the common belief that a magnet field enhances Wigner crystallization, the negative MR is likely linked to enhanced interaction.

Figure 1

(a) Schematics for the HIGFET, contacts, and measurement setup. (b) Band structure under gate voltage bias.

Figure 2

(a) Conductivity $\sigma$ vs $T$ in $log$ scales for various $p$ from 0.8 to $18\times {10}^9 {\text{cm}}^{-2}$. (b) Comparison of the resistivity $\rho$ vs $T$ (in $log$ scales) for selected $p$'s before and after disorder is introduced. Dotted lines are guides for the eye.

Figure 3

(a) ${\rho }_{xx}$ vs B for $p=1.2\times {10}^{10} {\mathrm{cm}}^{-2}$ at $T=45$ mK. (b) SdH oscillations seen in a zoom-in view of (a) at low fields. Inset: Fourier spectrum of the shown ${\rho }_{xx}\left(B\right)$.

Figure 4

(a) Low field magnetoresistance ${\rho }_{xx}\left(B\right)$ for various $p=$ (from top down) 0.24, 0.35, 0.45, 0.66, 0.85, 1.22, and $1.55\times {10}^{10}$ ${\mathrm{cm}}^{-2}$; (b) $\mathrm{\Delta }\rho =\rho \left(B\right)-\rho \left(0\right)$ vs $B$ for the same fixed $p$ shown in (a); (c) results in (b) normalized by $\rho \left(0\right)$. (d) $d\rho /dB$ vs $B$. (e) Results in (d) normalized by $\rho \left(0\right)$.