Effective g factor of low-density two-dimensional holes in a Ge quantum well

Abstract

We report measurements of the effective $g$ factor of low-density two-dimensional holes in a Ge quantum well. Using the temperature dependence of the Shubnikov-de Haas oscillations, we extract the effective $g$ factor in a magnetic field perpendicular to the sample surface. Very large values of the effective $g$ factor, ranging from $\sim13$ to $\sim28$, are observed in the density range of $1.4\times10^{10}$ cm$^{-2}$ to $1.4\times10^{11}$ cm$^{-2}$. When the magnetic field is oriented parallel to the sample surface, the effective $g$ factor is obtained from a protrusion in the magneto-resistance data that signifies full spin polarization. In the latter orientation, a small effective $g$ factor, $\sim1.3-1.4$, is measured in the density range of $1.5\times10^{10}$ cm$^{-2}$ to $2\times10^{10}$ cm$^{-2}$. This very strong anisotropy is consistent with theoretical predictions and previous measurements in other 2D hole systems, such as InGaAs and GaSb.