Nonlinear Meissner Effect in Disordered Superconductors

Theoretical results for the nonlinear Meissner screening current and field-dependence of the London penetration depth are reported as a function of temperature, external field, Fermi-surface anisotropy and disorder, the latter represented by the transport scattering rate 1/τ. The breaking of time-reversal symmetry by an imposed current leads to pair breaking by nonmagnetic impurities, and to suppression of the screening current that can be supported as the superconductor becomes increasingly disordered. Furthermore, the screening current is generally a nonlinear function of the condensate momentum. In the absence of vortices the Meissner current can be related to the gauge field in the region of the superconducting-vacuum interface j_s ∝ A (1 − θ |A|²/A_c²), where A is the vector potential. The mean pairing self energy, Δ, and Fermi velocity, v_f, determine the scale for the gauge field, A_c ∝ Δ/v_f. The dimensionless parameter, θ, determines the magnitude of the nonlinear current response and field dependence of the London penetration depth. For fully gapped BCS superconductors in the clean limit θ vanishes exponentially at low temperatures. Disorder decreases the superfluid fraction monotonically; however, θ remains finite at zero temperature and is a non-monotonic function of the pair-breaking parameter, α ∝ 1/τT_c, with a maximum near the cross-over to the dirty limit. We discuss new experimental signatures of the nonlinear current response for superconducting resonators and related devices.