Two - Dimensional Electron Liquid in a Weak Magnetic Field

Abstract

We present an effective theory describing the low-energy properties of an interacting 2D electron gas at large non-integer filling factors $ν\gg 1$. 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 $\hbarω_c$. The first energy scale, $(\hbarω_c/ν)\ln\left(νr_s\right)$, appears in the one electron spectral density as the width of a pseudogap. The second scale, $r_s\hbarω_c$, is parametrically larger; it characterizes the exchange-enhanced spin splitting and the thermodynamic density of states.