The electron effective mass in the strongly correlated 2D-uniform electron fluid from finite-temperature calculations

The very-low temperature thermal effective mass m* of paramagnetic and ferromagnetic electrons in a uniform electron fluid in two dimensions is studied. Analytical and numerical evaluations are used to meaningfully define an m*, even in the the Hartree-Fock approximation. The Hartree-Fock m* decreases linearly with the electron-disk radius r_s. Correlation effects lead to strong cancellations between exchange and correlation. Thus the effective mass is enhanced with increasing r_s for the unpolarized fluid, while m* decreases with the r_s of the polarized fluid. The effective mass is calculated from the coefficient of the quadratic temperature dependence of exchange-correlation free energy F_{xc}. This is calculated in a physically transparent manner using a new formula for the effective mass. This uses the T=0 pair-distribution functions of Gori-Giorgi et al., and the temperature derivative of a quantum analogue of the potential of mean-force well known in the statistical mechanics of classical fluids. The results are compared with recent quantum Monte-Carlo simulations at T=0, as well as with other available experimental and theoretical data for the effective mass.