Degeneracy and Effective Mass in the Valence Band of Two-Dimensional (100)-GaAs Quantum Well Systems

Quantum Hall measurement of two-dimensional high-mobility ($\mu\sim 2\times$ 10$^6$ cm$^2$/(V$\cdot$s)) hole systems confined in a 20 nm wide (100)-GaAs quantum well have been performed for charge densities between $4-5\times$ 10$^{10}$ cm$^{-2}$ in a temperature range of 10-160 mK. The Fourier analysis of the Shubnikov-de Haas (SdH) oscillations of the magnetoresistance vs. the inverse of the magnetic field $1/B_{\bot}$ reveals a single peak, indicating a degenerate heavy hole (HH) band. The corresponding hole density $p=(e/h)\cdot f$ agrees with the Hall measurement result within $3\%$. The HH degeneracy is understood through the diminishing Rashba spin-orbit interaction due to the low charge density and the nearly symmetric confinement. SdH oscillations fitted for 0.1 T $\leq B_{\bot} \leq 0.25 $ T to the Dingle parameters yield an effective mass ($m^*$) between 0.39 $m_e$ and 0.51 $m_e$ that increases moderately with increasing magnetic field and charge density, in very good agreement with previous cyclotron resonance measurements.