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

TL;DR

This paper investigates how electron correlations in a Wigner crystal influence interstitial energies and contribute to classical Hall resistivity, revealing that correlated interstitials destabilize the crystal near certain fillings.

Contribution

It introduces a trial wavefunction with Laughlin correlations for interstitials in a Wigner crystal, showing their role in destabilizing the crystal and explaining Hall resistivity.

Findings

Correlations lower interstitial energy near incompressible states

Interstitials destabilize the Wigner crystal near specific fillings

Correlated interstitials account for classical Hall resistivity

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 $\nu <1/m$ is introduced by constructing a trial wave- function which bears a Jastrow factor of a Laughlin state at $\nu=1/m$. For fillings close to but just below $\nu=1/m$, 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.