Low Frequency Nonlinear Magnetic Response of an Unconventional Superconductor

TL;DR

This paper investigates the nonlinear magnetic response of an unconventional superconductor at low frequencies, showing how harmonic analysis can reveal the superconductor's energy gap structure and distinguish between nodes and quasinodes.

Contribution

It introduces a method to analyze the field and angular dependence of nonlinear magnetic harmonics to determine the superconductor's gap symmetry and distinguish between nodal lines and quasinodes.

Findings

Nodal lines produce universal power law field dependences.

Quasinodes lead to complex, nonseparable field, temporal, and angular dependences.

Method to maximize nonlinear signals for gap symmetry investigation.

Abstract

We consider an unconventional superconductor in a low frequency harmonic magnetic field. In the Meissner regime at low T a nonlinear magnetic response arises from quasiparticle excitations near minima in the energy gap. Various physical quantities then acquire higher harmonics of the frequency of the applied field. We discuss how examination of the field and angular dependence of these harmonics allows determination of the structure of the energy gap. We show how to distinguish nodes from small finite minima ("quasinodes"). Gaps with nodal lines give rise to universal power law field dependences for the nonlinear magnetic moment and the nonlinear torque. They both have separable temporal and angular dependences. In contrast, when there are quasinodes these quantities have more complicated and nonseparable field, temporal, and angular dependences. We illustrate this on the example of an s+id gap. We discuss how to perform measurements so as to maximize the nonlinear signal and how to investigate in detail the properties of the superconducting minima, thus determining the gap function symmetry.