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 interband 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. arXiv:1710.09907v2 [cond-mat.supr-con]

We consider gauged skyrmions with boundary conditions which break the gauge from SU(2) to U(1) in models derived from Yang–Mills theory. After deriving general topological energy bounds, we approximate charge 1 energy minimisers using KvBLL calorons with non-trivial asymptotic holonomy, use them to calibrate the model to optimise the ratio of energy to lower bound, and compare them with solutions to full numerical simulation. Skyrmions from calorons with non-trivial asymptotic holonomy exhibit a non-zero magnetic dipole moment, which we calculate explicitly, and compare with experimental values for the proton and the neutron. We thus propose a way to develop a physically realistic Skyrme–Maxwell theory, with the potential for exhibiting low binding energies.

Multiband superconductors have a sufficient number of degrees of freedom to allow topological excitations characterized by Skyrmionic topological invariants. In the most common, clean s-wave multiband, systems the interband Josephson and magnetic couplings favours composite vortex solutions, without a Skyrmionic topological charge. It was discussed recently that certain kinds of anisotropies lead to hybridisation of the interband phase difference (Leggett) mode with magnetic modes, dramatically changing the hydromagnetostatics of the system. Here we report this effect for a range of parameters that substantially alter the nature of the topological excitations, leading to solutions characterized by a nontrivial Skyrmionic topological charge. The solutions have a form of a coreless texture formed of spatially separated but bound excitations in each band, namely fractional vortices, each carrying a fraction of the flux quantum. We demonstrate that in this regime there is a rich spectrum of Skyrmion solutions, with various topological charges, that are robust with respect to changes of parameters of the system and present for a wide range of anisotropies.