Quantum Correlated Interstitials and the Hall Resistivity of the Magnetically Induced Wigner Crystal

Abstract

We study a trial wavefunction for an interstitial in a Wigner crystal. We find that the electron correlations, ignored in a conventional Hartree-Fock treatment, dramatically lower the interstitial energy, especially at fillings close to an incompressible liquid state. The correlation between the interstitial electron and the lattice electrons at $ν<1/m$ is introduced by constructing a trial wave- function which bears a Jastrow factor of a Laughlin state at $ν=1/m$. For fillings close to but just below $ν=1/m$, we find that a perfect Wigner crystal becomes unstable against formation of such interstitials. It is argued that conduction due to correlated interstitials in the presence of weak disorder leads to the {\it classical} Hall resistivity, as seen experimentally.