Correlation energy of an electron gas in strong magnetic fields at high densities

TL;DR

This paper analyzes the correlation energy of a high-density electron gas in strong magnetic fields at zero temperature, focusing on the quantum limit where only the lowest Landau level is occupied, and derives an analogous perturbation series to the field-free case.

Contribution

It introduces a new expansion parameter r_B for the high-density electron gas in strong magnetic fields and derives the perturbation series up to first order in r_B for the quantum limit.

Findings

Perturbation series analogous to Gell-Mann Brueckner for magnetic fields

Exact expression up to o(r_B) for small Landau level filling

New expansion parameter r_B for high-density magnetic electron gas

Abstract

The high-density electron gas in a strong magnetic field B and at zero temperature is investigated. The quantum strong-field limit is considered in which only the lowest Landau level is occupied. It is shown that the perturbation series of the ground-state energy can be represented in analogy to the Gell-Mann Brueckner expression of the ground-state energy of the field-free electron gas. The role of the expansion parameter is taken by r_B= (2/3 \pi^2) (B/m^2) (\hbar r_s /e)^3 instead of the field-free Gell-Mann Brueckner parameter r_s. The perturbation series is given exactly up to o(r_B) for the case of a small filling factor for the lowest Landau level.