Hall Effect in the mixed state of moderately clean superconductors

TL;DR

This paper presents a microscopic analysis of the Hall effect in the mixed state of clean type-II superconductors, revealing how fluctuations and quasiparticle modifications influence the Hall conductivity and angle.

Contribution

It provides a detailed microscopic calculation of the Hall conductivity in the mixed state, highlighting the role of order parameter fluctuations and quasiparticle scattering.

Findings

Fluctuations' contribution to Hall conductivity is compensated by quasiparticle modifications.

The nonlinear Hall angle behavior is linked to changes in quasiparticle scattering rates.

Results are discussed in relation to experimental observations.

Abstract

The Hall conductivity in the mixed state of a clean ($l \gg \xi_0$) type-II s-wave superconductor is determined from a microscopic calculation within a quasiclassical approximation. We find that below the superconducting transition the contribution to the transverse conductivity due to dynamical fluctuations of the order parameter is compensated by the modification of the quasiparticle contribution. In this regime the nonlinear behaviour of the Hall angle is governed by the change in the effective quasiparticle scattering rate due to the reduction in the density of states at the Fermi level. The connection with experimental results is discussed.