Metal-insulator transition in dilute alkali-metal systems

Abstract

The metal-insulator transition is studied for dilute systems of alkali metals. Using a spin-split self-consistent band-structure approach, we find the transition density, a strikingly enhanced magnetic susceptibility, and the electron effective mass. The critical density ${n}_{c}$ is found to be given by the simple relation ${r}_{s}^{c}={r}_{0}+2.8$. Here ${r}_{s}^{c}={[\frac{3}{(4\ensuremath{\pi}{n}_{c}})]}^{\frac{1}{3}}$ and ${r}_{0}$ is the model potential radius which is roughly the radius of the neutral atom. The Mott criterion of ${n}_{c}^{\frac{1}{3}}{a}_{B}\ensuremath{\simeq}0.25$ (where ${a}_{B}$ is the appropriate Bohr orbit) is found to be inadequate for describing these systems. The predicted effective mass and magnetic susceptibility enhancements are largest for Li and become systematically smaller for the heavier alkalis. We compare our results for the transition density with two sets of experiments, namely the gas-liquid critical density and the metal-insulator transition for codeposited thick films of alkali-metal and rare-gas atoms. Good agreement is found in both cases.