Studies in the theory of multiband superconductors

Abstract

While the theory of multiband superconductivity has existed since the work of Suhl et al. and Moskalenko, it has only been with the discovery of superconductivity in magnesium diboride that this theory could be applied to real materials. The list of possible multiband superconductors has steadily grown, and these materials have attractive properties that warrant further investigation. In this thesis we look at two theories of multiband superconductivity and the connection between them. The first theory is the multiband generalisation of the microscopic theory of Bardeen, Cooper and Schrieffer (BCS). In the case of three superconducting bands, it is well known that there can exist a phase transition to a new phase of superconductivity, the time-reversal-symmetry-broken (TRSB) state. We show that in this state the full multiband theory reduces exactly to solving a set of independent one-band equations. In addition, this reduction produces a set of conditions among these one-band solutions which must be satisfied for them to be solutions of the full multiband equations. These conditions can therefore be used to find the TRSB transition temperature. The phenomenological Ginzburg-Landau theory (GL), which can be derived as an expansion of BCS theory around the critical temperature, has also had a multiband generalisation which was first derived by Tilley. Peeter’s and co-workers recently used the Gor’kov technique to find the next order corrections to the theory, extending the validity to slightly lower temperatures. We restrict ourselves to the field-free case and find extensions to very high order. We show that in the one-band theory and most multiband cases the superconducting gap in this extended GL theory converges to the BCS theory over almost the entire temperature range. However there are some cases in the multiband theory where the GL expansion diverges. This divergence is related to the appearance of a second critical temperature in the uncoupled limit. Finally we apply a range of numerical methods to find vortex and skyrmion states in multiband superconductors. The skyrmion states are variations of the well-known vortex states, and only appear when the bulk superconductor is in the TRSB state. We find that, with the bulk in the TRSB state, the low order skyrmion solutions are very robust and are very likely to evolve from a random initial configuration. However the higher order skyrmion states are instead likely to form a collection of lower order skyrmions and vortices, and a large amount of control is required to form them. Show more