Hall map and breakdown of Fermi liquid theory in the vicinity of a Mott insulator

TL;DR

This paper investigates the anomalous Hall effect in lightly doped Mott insulators, revealing a divergence and sign reversal near the Mott transition, and links the Hall current to spin-entangled vacancies potentially related to superconductivity.

Contribution

It provides a detailed calculation of the Hall coefficient's doping and temperature dependence in the tJ-model, including quantum Monte Carlo results and insights into the nature of charge carriers near the Mott insulator.

Findings

Hall coefficient diverges near the Mott limit

Sign reversal of the Hall coefficient compared to weak scattering predictions

Hall current carried by spin-entangled vacancies potentially forming Cooper pairs

Abstract

The Hall coefficient exhibits anomalous behavior in lightly doped Mott insulators. For strongly interacting electrons its computation has been challenged by analytical and numerical obstacles. We calculate the leading contributions in the recently derived thermodynamic formula for the Hall coefficient. We obtain its doping and temperature dependence for the square lattice tJ-model at high temperatures. The second order corrections are evaluated to be negligible. Quantum Monte Carlo sampling extends our results to lower temperatures. We find a divergence of the Hall coefficient toward the Mott limit and a sign reversal relative to Boltzmann equation's weak scattering prediction. The Hall current near the Mott phase is carried by a low density of spin-entangled vacancies, which should constitute the Cooper pairs in any superconducting phase at lower temperatures.