Field- and temperature-induced topological phase transitions in the three-dimensionalN-component London superconductor

Abstract

The phase diagram and critical properties of the $N$-component London superconductor are studied both analytically and through large-scale Monte Carlo simulations in $d=2+1$ dimensions (components here refer to different replicas of the complex scalar field). Examples are given of physical systems to which this model is applicable. The model with different bare phase stiffnesses for each component is a model of superconductivity, which should arise out of metallic phases of light atoms under extreme pressure. A projected mixture of electronic and protonic condensates in liquid metallic hydrogen under extreme pressure is the simplest example, corresponding to $N=2$. These are such that Josephson coupling between different matter field components is precisely zero on symmetry grounds. The $N$-component London model is dualized to a theory involving $N$ vortex fields with highly nontrivial interactions. We compute critical exponents $\ensuremath{\alpha}$ and $\ensuremath{\nu}$ for $N=2$ and $N=3$. Direct and dual gauge field correlators for general $N$ are given and the $N=2$ case is studied in detail. The model with $N=2$ shows two anomalies in the specific heat when the bare phase stiffnesses of each matter field species are different. One anomaly corresponds to an inverted $3\mathrm{D}xy$ fixed point, while the other corresponds to a $3\mathrm{D}xy$ fixed point. Correspondingly, for $N=3$, we demonstrate the existence of two neutral $3\mathrm{D}xy$ fixed points and one inverted charged $3\mathrm{D}xy$ fixed point. For the general case, there are $N$ fixed points, namely one charged inverted $3\mathrm{D}xy$ fixed point, and $N\ensuremath{-}1$ neutral $3\mathrm{D}xy$ fixed points. We explicitly identify one charged vortex mode and $N\ensuremath{-}1$ neutral vortex modes. The model for $N=2$ and equal bare phase stiffnesses corresponds to a field theoretical description of an easy-plane quantum antiferromagnet. In this case, the critical exponents are computed and found to be non-$3\mathrm{D}xy$ values. The $N$-component London superconductor model in an external magnetic field, with no interspecies Josephson coupling, will be shown to have a different feature, namely $N\ensuremath{-}1$ superfluid phases arising out of $N$ charged condensates. In particular, for $N=2$ we point out the possibility of two different types of field-induced phase transitions in ordered quantum fluids: (i) A phase transition from a superconductor to a superfluid or vice versa, driven by tuning an external magnetic field. This sets the superconducting phase of liquid metallic hydrogen apart from other known quantum fluids. (ii) A phase transition corresponding to a quantum fluid analogue of sublattice melting, where a composite field-induced Abrikosov vortex lattice is decomposed and disorders the phases of the constituent condensate with lowest bare phase stiffness. Both transitions belong to the $3\mathrm{D}xy$ universality class. For $N\ensuremath{\geqslant}3$, there is a feature not present in the cases $N=1$ and $N=2$, namely a partial decomposition of composite field-induced vortices driven by thermal fluctuations. A ``color electric charge'' concept, useful for establishing the character of these phase transitions, is introduced.