Effective mass of quasiparticles in a Wigner liquid

The exchange interaction and effective mass of fermionic excitation in a low-density (rS ≫ 1) system of two-dimensional electrons are estimated from simple considerations. For the ratio of effective (renormalized due to interaction) to band mass, the dependence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${{m^* } \mathord{\left/ {\vphantom {{m^* } m}} \right. \kern-\nulldelimiterspace} m} = ({A \mathord{\left/ {\vphantom {A {\sqrt {r_S } }}} \right. \kern-\nulldelimiterspace} {\sqrt {r_S } }})\exp (\alpha \sqrt {r_S } )$$ \end{document} is obtained, where A and α are constants on the order of unity. The effective g factor is independent of rS and is larger than its bare value in the two-valley case (silicon). Comparison with experimental data shows a qualitative agreement with silicon.