Two - Dimensional Electron Liquid in a Weak Magnetic Field

TL;DR

This paper develops an effective theory for a weakly interacting two-dimensional electron gas at high filling factors, revealing two key energy scales that govern low-energy electron dynamics and spectral properties.

Contribution

It introduces a novel effective Hamiltonian for large non-integer filling factors, capturing low-energy behaviors and identifying two distinct energy scales in the system.

Findings

Identification of the pseudogap width as $( abla ext{hbar}\omega_c/ u)\ln( u r_s)$

Discovery of a larger energy scale $r_s ext{hbar}\omega_c$ for spin splitting

Characterization of the thermodynamic density of states at low energies

Abstract

We present an effective theory describing the low-energy properties of an interacting 2D electron gas at large non-integer filling factors $\nu\gg 1$. Assuming that the interaction is sufficiently weak, $r_s < 1$, we integrate out all the fast degrees of freedom, and derive the effective Hamiltonian acting in the Fock space of the partially filled Landau level only. This theory enables us to find two energy scales controlling the electron dynamics at energies less than $\hbar\omega_c$. The first energy scale, $(\hbar\omega_c/\nu)\ln\left(\nu r_s\right)$, appears in the one electron spectral density as the width of a pseudogap. The second scale, $r_s\hbar\omega_c$, is parametrically larger; it characterizes the exchange-enhanced spin splitting and the thermodynamic density of states.