Multicomponent dense electron gas as a model of Si MOSFET

TL;DR

This paper models a multicomponent dense electron gas in two dimensions, analyzing its ground state, effective mass, and quantum Hall properties in the large N limit and specific interaction regimes.

Contribution

It introduces a solvable model for a multicomponent electron gas, providing analytical expressions for energy, effective mass, and quantum Hall gaps in the large N limit.

Findings

Ground state energy and effective mass expressed as series in powers of r_s^{2/3}

Quasiparticle interaction on the Fermi circle vanishes as 1/N

Charge activation energy gap and exchange constant calculated for quantum Hall state

Abstract

We solve two-dimensional model of $N$-component dense electron gas in the limit of large $N$ and in a range of the Coulomb interaction parameter: $N^{-3/2}\ll r_s\ll 1$. The quasiparticle interaction on the Fermi circle vanishes as 1/N. The ground state energy and the effective mass are found as series in powers of $r_s^{2/3}$. In the quantum Hall state on the lowest Landau level at integer filling: $1\ll\nu<N$, the charge activation energy gap and the exchange constant are found.