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

TL;DR

This study uses diffusion Monte Carlo to analyze a multi-valley electron gas in semiconductors, validating analytical models and applying them to quantum dots with high valley degeneracy.

Contribution

It provides a detailed DMC analysis of a multi-valley electron gas and extends analytical models to inhomogeneous systems for quantum dot applications.

Findings

DMC results agree within 1% with analytic energy expressions across densities.

Distinguished between exact and approximate polarizability expressions for high valley degeneracy.

Gradient correction improves the analytical model's accuracy in inhomogeneous systems.

Abstract

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 Bi2Te3 (six-fold valley degeneracy) the applicable charge carrier densities are between 7*10^19cm^{-3} and 2*10^20cm^{-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 with DMC results for a quantum dot.