Motion of Vacancies in a Pinned Vortex Lattice: Origin of the Hall Anomaly

TL;DR

This paper explains the Hall anomaly in superconductors as a result of vortex many-body correlations, providing a quantitative analysis of vortex vacancy formation energy and resistivity scaling near the transition temperature.

Contribution

It introduces a physical argument linking the Hall anomaly to vortex correlations and derives a quantitative vortex vacancy formation energy for thin films.

Findings

Hall anomaly arises from vortex many-body effects

A scaling relation between Hall and longitudinal resistivities is established

Hall conductivity near transition temperature is proportional to inverse magnetic field and quadratic temperature difference

Abstract

Physical arguments are presented to show that the Hall anomaly is an effect of the vortex many-body correlation rather than that of an individual vortex. Quantitatively, the characteristic energy scale in the problem, the vortex vacancy formation energy, is obtained for thin films. At low temperatures a scaling relation between the Hall and longitudinal resistivities is found, with the power depending on sample details. Near the superconducting transition temperature and for small magnetic fields the Hall conductivity is found to be proportional to the inverse of the magnetic field and to the quadratic of the difference between the measured and the transition temperatures.