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

Abstract

A many-flavor electron gas ͑MFEG͒ in a semiconductor with a valley degeneracy ranging between 6 and 24 was analyzed using diffusion Monte Carlo ͑DMC͒ calculations. The DMC results compare well to an analytic expression derived by one of us ͓Phys. Rev. B 78, 035111 ͑2008͔͒ for the total energy to within Ϯ1% over an order of magnitude range of density, which increases with valley degeneracy. For Bi 2 Te 3 ͑sixfold valley degeneracy͒ the applicable charge-carrier densities are between 7 ϫ 10 19 cm −3 and 2 ϫ 10 20 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 Ͻ q Ͻ 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.