Diffusion Monte Carlo study of a valley-degenerate electron gas and application to quantum dots

A many-flavor electron gas (MFEG) in a semiconductor with a valley degeneracy ranging between 6 and 24 was analyzed using diffusion Monte Carlo (DMC) calculations. The DMC results compare well to an analytic expression derived by one of us [ Phys. Rev. B 78 035111 (2008)] for the total energy to within ±1% over an order of magnitude range of density, which increases with valley degeneracy. For Bi₂Te₃ (sixfold valley degeneracy) the applicable charge-carrier densities are between 7×10¹⁹ cm⁻³ and 2×10²⁰ cm⁻³. DMC calculations distinguished between an exact and a useful approximate expression for the 24-fold degenerate MFEG polarizability for wave numbers 2p_F<q<7p_F. The analytical result for the MFEG is generalized to inhomogeneous systems by means of a gradient correction; the validity range of this approach is obtained. Employed within a density-functional theory calculation this approximation compares well to DMC results for a quantum dot.