Structure formation, phase transitions and drag interactions in multicomponent superconductors and superfluids

Abstract: Superconductivity and superfluidity are some of the most funda-mental and important phenomena of modern physics. However, muchtheoretical work for such systems so far has been restricted to the one-component case. For multicomponent systems, the spectrum of possible topological defects, their structure formation and associated phasetransitions, 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 point-particle Monte Carlo simulations. Besides the triangular vortex latticesfound for one-component type-2 superconducting vortices, it is found that a rich plethora of structural phases is possible for vortices in mul-ticomponent systems.Since vortices play a key role in phase transitions, the problem of phase transitions in multicomponent systems is also studied in thisthesis. It could be expected that U(1) lattice London superconductorscan only have a continuous “inverted-XY” phase transition by a Peskin-Dasgupta-Halperin duality argument for the one-component case. Itis 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, wherein 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 com-posite vortices to decay into attractively interacting skyrmions. Suchdrag interactions can to a large extent influence phase transitions, rotational response and vortex structures in multicomponent systems. Thisthesis thus finishes with microscopic calculations of such an Andreev-Bashkin drag interaction in an extended Bose-Hubbard model of two-species bosons in an optical lattice, using worm quantum Monte Carlosimulations. Dependencies of the drag interaction on boson-boson in-teractions and properties of the optical lattice are characterized, andpaired phases (where only co- or counter-flow states occur) are observed.