Non-London electrodynamics in a multiband London model: anisotropy-induced non-localities and multiple magnetic field penetration lengths

TL;DR

This paper explores how anisotropy in multiband London superconductors leads to multiple and complex magnetic field penetration lengths, resulting in non-local magnetic responses and novel vortex states.

Contribution

It reveals that anisotropy induces multiple, possibly complex, magnetic penetration lengths and hybridizes London and Leggett modes, which was not previously understood in multiband superconductors.

Findings

Multiple penetration lengths in anisotropic multiband models.

Existence of complex magnetic modes with oscillatory decay.

Non-monotonic magnetic field decay and vortex bound states.

Abstract

The London model describes strongly type-2 superconductors as massive vector field theories, where the magnetic field decays exponentially at the length scale of the London penetration length. This also holds for isotropic multi-band extensions, where the presence of multiple bands merely renormalises the London penetration length. We show that, by contrast, the magnetic properties of anisotropic multi-band London models are not this simple, and the anisotropy leads to the inter-band phase differences becoming coupled to the magnetic field. This results in the magnetic field in such systems having N+1 penetration lengths, where N is the number of field components or bands. That is, in a given direction, the magnetic field decay is described by N+1 modes with different amplitudes and different decay length scales. For certain anisotropies we obtain magnetic modes with complex masses. That means that magnetic field decay is not described by a monotonic exponential increment set by a real penetration length but instead is oscillating. Some of the penetration lengths are shown to diverge away from the superconducting phase transition when the mass of the phase-difference mode vanishes. Finally the anisotropy-driven hybridization of the London mode with the Leggett modes can provide an effectively non-local magnetic response in the nominally local London model. Focusing on the two-component model, we discuss the magnetic field inversion that results from the effective non-locality, both near the surface of the superconductor and around vortices. In the regime where the magnetic field decay becomes non-monotonic, the multiband London superconductor is shown to form weakly-bound states of vortices.