Low-frequency nonlinear magnetic response of an unconventional superconductor

We consider an unconventional superconductor in a low-frequency harmonic magnetic field. In the Meissner regime at low temperatures a nonlinear magnetic response arises from quasiparticle excitations near minima in the energy gap. As a consequence various physical quantities acquire higher harmonics of the frequency of the applied ac field. We discuss how an examination of the field and angular dependences of these harmonics allows the 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 magnetic torque. They both have separable temporal and angular dependences. In contrast, with gap functions which only have quasinodes, these physical quantities do not display power laws in the applied field, and their temporal and angular dependences are no longer separable. We illustrate this via the example of the nonlinear magnetic moment for a $d+is$ gap. We discuss how to perform ac 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.