Structure formation, phase transitions and drag interactions in multicomponent su- perconductors and superfluids

Superconductivity and superfluidity are some of the most fundamental and important phenomena of modern physics. However, much theoretical work for such systems so far has been restricted to the onecomponent case. For multicomponent systems, the spectrum of possible topological defects, their structure formation and associated phase transitions, can all be much richer than in the one-component case, motivating theoretical studies of multicomponent systems. In this thesis, the structure formation of vortices with complicated interactions due to multicomponent effects are considered using pointparticle Monte Carlo simulations. Besides the triangular vortex lattices found for one-component type-2 superconducting vortices, it is found that a rich plethora of structural phases is possible for vortices in multicomponent systems. Since vortices play a key role in phase transitions, the problem of phase transitions in multicomponent systems is also studied in this thesis. It could be expected that U(1) lattice London superconductors can only have a continuous “inverted-XY” phase transition by a PeskinDasgupta-Halperin duality argument for the one-component case. It is discussed here that the non-trivial internal structure of vortices in multicomponent U(1) London superconductors can instead lead to a first-order phase transition, which is supported by large-scale parallel tempering Monte Carlo simulations. Even for such systems, where in the ground state vortex lines are axially symmetric, thermally induced splitting of composite vortices into fractional vortices can lead to a phase separation of vortex tangles, rendering the superconducting phase transition first-order. A similar phase separation can occur for two-component superconductors with an Andreev-Bashkin drag interaction, for which a phase separation can occur even in the ground state: the drag can cause composite vortices to decay into attractively interacting skyrmions. Such drag interactions can to a large extent influence phase transitions, rotational response and vortex structures in multicomponent systems. This thesis thus finishes with microscopic calculations of such an AndreevBashkin drag interaction in an extended Bose-Hubbard model of twospecies bosons in an optical lattice, using worm quantum Monte Carlo simulations. Dependencies of the drag interaction on boson-boson interactions and properties of the optical lattice are characterized, and paired phases (where only coor counter-flow states occur) are observed.