Anderson Localization of Electrons in DenseHe4Gas

The conductance of a dilute 2D electron gas on hydrogen is measured as a function of ambient ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ gas density. At densities below ≅ ${10}^{20}$ ${\mathrm{cm}}^{-3\mathrm{}}$ the electron scattering rate is the sum of a classical term linear in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ density plus a ${}_{}{}^4{}_{}{}^{}\mathrm{He}$-adsorbate-scattering term. Towards higher densities, however, the conductivity decreases exponentially which we attribute to strong localization of electrons below a threshold energy $E_c\gtrsim k_{\mathrm{B}}T$. We present an estimate of $E_c$ based on weak-localization theory and find good agreement with both our 2D data and the 3D mobility measurements in the literature. In 3D, the Ioffe-Regel criterion for localization is found to be $k{l}_0=2.5\mathrm{}\pm 0.5$.