Strong Spin-Orbit Contribution to the Hall Coefficient of Two-Dimensional Hole Systems

Classical charge transport, such as longitudinal and Hall currents in weak magnetic fields, is usually not affected by quantum phenomena. Yet relativistic quantum mechanics is at the heart of the spin-orbit interaction, which has been at the forefront of efforts to realize spin-based electronics, new phases of matter, and topological quantum computing. In this work we demonstrate that quantum spin dynamics induced by the spin-orbit interaction is directly observable in classical charge transport. We determine the Hall coefficient $R_H$ of two-dimensional hole systems at low magnetic fields and show that it has a sizable spin-orbit contribution, which depends on the density $p$, is independent of temperature, is a strong function of the top gate electric field, and can reach $\sim 20\%$ of the total. We provide a general method for extracting the spin-orbit parameter from magnetotransport data, applicable even at higher temperatures where Shubnikov–de Haas oscillations and weak antilocalization are difficult to observe. Our work will enable experimentalists to measure spin-orbit parameters without requiring large magnetic fields, ultralow temperatures, or optical setups.

Figure 1

Spin-orbit correction to the Hall coefficient $R_H$ for various 15 nm quantum wells as a function of the perpendicular electric field $F_z$, where $R_0\equiv 1/pe$ is the bare Hall coefficient. Panel shows results for (a) different materials at $p=1.5\times {10}^{11}{\mathrm{cm}}^{-2}$ and (b) GaAs quantum wells at different densities.

Figure 2

The Rashba coefficient $\beta$ of as a function of the net perpendicular electric field $F_z$ for 15 nm GaAs, InAs, and InSb quantum wells. The inset shows that $\beta$ for GaAs decreases by $\sim 20\%$ as $F_z$ is increased from $4\mathrm{MV}/\mathrm{m}$ to $10\mathrm{MV}/\mathrm{m}$, as the well becomes quasitriangular at $F_z\gtrsim 4\mathrm{MV}/\mathrm{m}$.

Figure 3

Ratio of Drude conductivity at finite perpendicular electric fields ($F_z$) to its zero electric field value ($F_z=0$), with the bare Drude conductivity ${\sigma }_0\equiv pe\mu$, for (a) different quantum well materials at $p=1.5\times {10}^{11}{\mathrm{cm}}^{-2}$ and (b) GaAs quantum wells at different densities. The well width is 15 nm.