Multicomponent superconductivity Vortex matter and phase transitions

Abstract: The topic of this thesis is vortex-physics in multi component Ginzburg- Landau models. These models describe a newly discovered class of super- conductors with multiple superconducting gaps, and possess many properties that set them apart from single component models. The work presented here relies on large scale computer simulations using various numerical techniques, but also on some analytical methods.In Paper I, Type-1.5 Superconducting State from an Intrinsic Proximity Effect in Two-Band Superconductors, we show that in multiband supercon- ductors, even an extremely small interband proximity effect can lead to a qualitative change in the interaction potential between superconducting vor- tices, by producing long-range intervortex attraction. This type of vortex interaction results in an unusual response to low magnetic fields, leading to phase separation into domains of two-component Meissner states and vortex droplets.In paper II, Type-1.5 superconductivity in two-band systems, we discuss the influence of Josephson coupling and show that non-monotonic intervortex interaction can also arise in two-band superconductors where one of the bands is proximity induced by Josephson interband coupling.In paper III, Type-1.5 superconductivity in multiband systems: Effects of interband couplings, we investigate the appearance of Type-1.5 superconduc- tivity in the case with two active bands and substantial inter-band couplings such as intrinsic Josephson coupling, mixed gradient coupling, and density- density interactions. We show that in the presence of these interactions, the system supports type-1.5 superconductivity with fundamental length scales being associated with the mass of the gauge field and two masses of normal modes represented by linear combinations of the density fields.In paper IV, Semi-Meissner state and nonpairwise intervortex interactions in type-1.5 superconductors, we demonstrate the existence of nonpairwise in- tervortex forces in multicomponent and layered superconducting systems. We also consider the properties of vortex clusters in a semi-Meissner state of type- 1.5 two-component superconductors. We show that under certain conditions nonpairwise forces can contribute to the formation of complex vortex states in type-1.5 regimes.In paper V, Length scales, collective modes, and type-1.5 regimes in three- band superconductors, we consider systems where frustration in phase dif- ferences occur due to competing Josephson inter-band coupling terms. We show that gradients of densities and phase differences can be inextricably intertwined in vortex excitations in three-band models. This can lead to long-range attractive intervortex interactions and the appearance of type-1.5 regimes even when the intercomponent Josephson coupling is large. We also show that field-induced vortices can lead to a change of broken symmetry from U (1) to U (1) ? Z2 in the system. In the type-1.5 regime, it results in a semi-Meissner state where the system has a macroscopic phase separation in domainswithbrokenU(1)andU(1)?Z2 symmetries.In paper VI, Topological Solitons in Three-Band Superconductors with Broken Time Reversal Symmetry, we show that three-band superconductors with broken time reversal symmetry allow magnetic flux-carrying stable topo- logical solitons. They can be induced by fluctuations or quenching the system through a phase transition. It can provide an experimental signature of the time reversal symmetry breakdown.In paper VII, Type-1.5 superconductivity in multiband systems: Magnetic response, broken symmetries and microscopic theory – A brief overview, we give an overview of vortex physics and magnetic response in multi component Ginzburg-Landau theory. We also examine Type-1.5 superconductivity in the context of microscopic theory.In paper VIII, Chiral CP2 skyrmions in three-band superconductors, we show that under certain conditions, three-component superconductors (and, in particular, three-band systems) allow stable topological defects different from vortices. We demonstrate the existence of these excitations, charac- terised by a CP2 topological invariant, in models for three-component super- conductors with broken time-reversal symmetry. We term these topological defects “chiral GL(3) skyrmions,” where “chiral” refers to the fact that due to broken time-reversal symmetry, these defects come in inequivalent left- and right-handed versions. In certain cases, these objects are energetically cheaper than vortices and should be induced by an applied magnetic field. In other situations, these skyrmions are metastable states, which can be produced by a quench. Observation of these defects can signal broken time-reversal sym- metry in three-band superconductors or in Josephson-coupled bilayers of s± and s-wave superconductors.In paper IX, Phase transition in multi-component superconductors, we ex- amine the thermodynamics of frustrated multi-components superconductors and show that their highly complex energy landscape can give rise new types of phase transitions not present in single component superconductors.