Physical Review B **78**, 195310 (2008)
# Diffusion Monte Carlo study of a valley degenerate electron gas and application to quantum dots

G. J. Conduit^{1} and P. D. Haynes^{2}
^{1}*Theory of Condensed Matter, Department of Physics,
University of Cambridge, Cavendish Laboratory,
19 J. J. Thomson Avenue, Cambridge CB3 0HE,
UK*

^{2}*Departments of Physics and Materials,
Imperial College London, Exhibition Road, London SW7 2AZ, UK*

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 with 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 Bi_{2}Te_{3} (six-fold valley
degeneracy) the applicable charge carrier densities are between
7×10^{19} cm^{-3} and 2×10^{20}
cm^{-3}. DMC calculations distinguished between an exact and a
useful approximate expression for the 24-fold degenerate MFEG
polarizability for wave numbers 2*p*_{F} < *q* <
7*p*_{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 with DMC results for a quantum dot.

Last updated: 5 August 2010