We use analytical arguments and large-scale Monte Carlo calculations to investigate the nature of the phase transitions between distinct complex superfluid phases in a two-component Bose-Einstein condensate when a non-dissipative drag between the two components is being varied. We focus on understanding the role of topological defects in various phase transitions and develop vortex-matter arguments allowing an analytical description of the phase diagram. We find the behavior of fluctuation induced vortex matter to be much more complex and substantially different from that of single-component superfluids. We propose and investigate numerically a novel drag-induced "preemptive vortex loop proliferation" transition. Such a transition may be a quite generic feature in many multicomponent systems where symmetry is restored by a gas of several kinds of competing vortex loops.

We have performed large-scale Monte Carlo simulations on a two-dimensional generalized Ashkin-Teller model to calculate the thermodynamic properties in the critical region near its transitions. The Ashkin-Teller model has a pair of Ising spins at each site which interact with neighboring spins through pair-wise and four-spin interactions. The model represents the interactions between orbital current loops in CuO 2 plaquettes of high-T c cuprates, which order with a staggered magnetization M s inside each unit cell in the underdoped region of the phase diagram below a temperature T ‫ء‬ ͑x͒ which depends on doping. The pair of Ising spins per unit cell represents the directions of the currents in the links of the current loops. The generalizations are the inclusion of anisotropy in the pair-wise nearest-neighbor current-current couplings consistent with the symmetries of a square lattice and the next-nearest-neighbor pair-wise couplings. We use the Binder cumulant to estimate the correlation length exponent and the order-parameter exponent ␤. Our principal results are that in a range of parameters; the Ashkin-Teller model as well as its generalization has an order-parameter susceptibility which diverges as T → T ‫ء‬ and an order parameter below T ‫ء‬ . Importantly, however, there is no divergence in the specific heat. This puts the properties of the model in accord with the experimental results in the underdoped cuprates. We also calculate the magnitude of the "bump" in the specific heat in the critical region to put limits on its observability. Finally, we show that the staggered magnetization couples to the uniform magnetization M 0 such that the latter has a weak singularity at T ‫ء‬ and also displays a wide critical region, also in accord with recent experiments.

We study the evolution of rotational response of a hydrodynamic model of a two-component superfluid with a non-dissipative drag interaction, as the system undergoes a transition into a paired phase at finite temperature. The transition manifests itself in a change of (i) vortex lattice symmetry, and (ii) nature of vortex state. Instead of a vortex lattice, the system forms a highly disordered tangle which constantly undergoes merger and reconnecting processes involving different types of vortices, with a "hidden" breakdown of translational symmetry.Comment: 4 pages, 5 figs. Submitted to Physical Review. Online suppl. material available; Ref. 6. V2: Fig. 1 re-sent, URL in Ref. 6 correcte

We derive a Ginzburg-Landau free energy for a p-wave ferromagnetic superconductor. The starting point is a microscopic Hamiltonian including a spin generalised BCS term and a Heisenberg exchange term. We find that coexistence of magnetisation and superconductivity depends on the sign of the energy-gradient of the DOS at Fermi level. We also compute the tunneling contribution to the Ginzburg-Landau free energy, and find expressions for the spin-currents and Josephson currents across a tunneling junction separating two ferromagnetic p-wave superconductors.

In a single-component superfluid under rotation a broken symmetry in the order parameter space results in a broken translational symmetry in real space: a vortex lattice. If translational symmetry is restored, the phase of the order parameter disorders and thus the broken symmetry in the order parameter space is also restored. We show that for Bose-Einstein condensate mixtures in optical lattices with negative dissipationless drag, a new situation arises. This state is a modulated vortex liquid which breaks translational symmetry in the direction transverse to the rotation vector.