Many-flavor electron gas approach to electron-hole drops

TL;DR

This paper develops a theoretical framework for a many-flavor electron gas in multi-valley semiconductors, deriving energy expressions and applying a local density approximation to analyze electron-hole drops.

Contribution

It provides an exact energy expression for the MFEG and introduces a gradient expansion approach to study electron-hole drops, revealing new density profiles and surface properties.

Findings

Derived an exact total energy expression for the MFEG.

Developed a local density approximation with gradient expansion.

Found new density profile and surface scaling for electron-hole drops.

Abstract

A many-flavor electron gas (MFEG) is analyzed, such as could be found in a multi-valley semiconductor or semimetal. Using the re-derived polarizability for the MFEG an exact expression for the total energy of a uniform MFEG in the many-flavor approximation is found; the interacting energy per particle is shown to be -0.574447E_h a_0^3/4 m*^3/4 n^1/4 with E_h being the Hartree energy, a_0 Bohr radius, and m^* particle effective mass. The short characteristic length-scale of the MFEG motivates a local density approximation, allowing a gradient expansion in the energy density, and the expansion scheme is applied to electron-hole drops, finding a new form for the density profile and its surface scaling properties.