Theory of Hall Anomaly in the Mixed State

TL;DR

This paper presents a theoretical framework explaining the Hall anomaly in the mixed state of superconductors as a vortex many-body correlation effect, accounting for sign changes and scaling behaviors.

Contribution

It introduces a vortex many-body effect model that explains the Hall anomaly, including sign reversal and quantitative relationships with resistivities and temperature.

Findings

Hall anomaly arises from vortex vacancies and interstitials competition.

Derived expression for vortex vacancy formation energy.

Found scaling relation between Hall and longitudinal resistivities.

Abstract

Analogous to Peierls' arguments for the `anomalous' Hall in metals I demonstrate that the Hall anomaly in the mixed state of superconductors, the sign change of the Hall resistivity, is a property of a vortex many-body correlation, and show that the anomaly is due to the competition between vortex vacancies and interstitials. Within this vortex many-body effect picture, many features of the complicated Hall effect can be understood in quantitative terms. For example, the expression for the vacancy formation energy is obtained, the scaling relation between the Hall and longitudinal resistivities with the power varying between 1 and 2 is found to depend on sample details, and near the superconducting transition temperature and for small magnetic fields the Hall conductivity is proportional to the inverse of the magnetic field and to the quadratic of the difference between the measured and the transition temperatures.