While the properties of standard (single-component) superfluids are well understood, principal differences arise in a special type of multicomponent systems - the so-called Borromean supercounterfluids - in which (i) supertransport is possible only in the counterflow regime and (ii) there are three or more counterflowing components. Borromean supercounterfluids's correlation and topological properties distinguish them from their single- and two-component counterparts. The component-symmetric case characterized by a distinctively different universality class of the supercounterfluid-to-normal phase transition is especially interesting. Using the recently introduced concept of compact-gauge invariance as the guiding principle, we develop the finite-temperature description of Borromean supercounterfluids in terms of an asymptotically exact long-wave effective action. We formulate and study Borromean XY and loop statistical models, capturing the universal long-range properties and allowing us to perform efficient worm algorithm simulations. Numeric results demonstrate perfect agreement with analytic predictions. Particularly instructive is the two-dimensional case, where the Borromean nature of the system is strongly manifested while allowing for an asymptotically exact analytic description.

Using a microscopic approach, we revisit the problem of superconducting critical temperature change in the presence of twin boundaries. We show that both critical temperature enhancement and suppression can come purely from single-electron geometric effects. These include aspects of scattering of electrons on these crystalline defects even when the coupling constant is unchanged. We consider two-dimensional rectangular and three-dimensional body-centered-cubic lattices with on-site s-wave superconducting pairing, nearest- and next-nearest-neighbor hoppings. In the considered two-dimensional lattice with twin boundaries, the superconducting critical temperature associated with twinning planes is suppressed for moderate band filling and enhanced for an almost empty or filled band. The superconducting phase diagram is more diverse for the three-dimensional lattice, which is caused by the interplay of van Hove singularity, changing coordination number, and modification of distances to nearest and next-nearest neighbors.

In conventional type-II superconductors, quantum vortices determine the magnetic response of the system and tend to form regular lattices. UTe2 is a recently discovered heavy Fermion superconductor exhibiting many anomalous macroscopic behaviors, but whether it has a multicomponent order parameter remains open. Here, we study the vortices of UTe2 by employing scanning superconducting quantum interference device microscopy. While a small out-of-plane magnetic field produces typical isolated vortices, a higher field generates vortex stripe patterns that evolve with the vortex density. The stripes form at different locations and along different directions in the surface plane when the field is along the b or c axis. The behavior is reproduced by our simulation based on an anisotropic two-component order parameter. This study shows that UTe2 has a nontrivial disparity of multiple length scales, placing constraints on the multicomponent superconductivity.

We predict a topological defect in perfectly screened ferroelectric barium titanate which we call a skyrme line. These are linelike objects characterized by skyrmionic topological charge. As well as configurations with integer topological charge, the charge density can split into well-localized parts carrying a localized fraction of topological charge. We show that under certain conditions the fractional skyrme lines are stable. We discuss a mechanism to create fractional topological charge objects and investigate their stability.

Counterflow superfluidity in a system with N≥3 components is distinctively different from the N=2 case. The key feature is the difference between the number (N) of elementary vortex excitations and the number (N-1) of independent branches of phonon modes, that is, the number of superfluid modes is larger than the number of ordered phase variables. We formulate a hydrodynamic theory of this state. We show how all the dynamical and statistical aspects of this ("Borromean") type of ordering are naturally described by effective N-component theory featuring compact-gauge invariance. We also discuss how off diagonal intercomponent couplings convert the Borromean supercounterfluid into a Borromean insulator, with an emphasis on the properties of a nontrivial state with broken time-reversal symmetry.

Two-band superconductors exhibit a distinct phase characterized by two correlation lengths, one smaller and the other larger than the magnetic field penetration length. This regime was coined type-1.5 superconductivity, with several unconventional properties, such as vortex clustering. However, a fully microscopic solution for vortex clusters has remained challenging due to computational complexities beyond quasiclassical models. This work presents numerical solutions obtained in a fully self-consistent two-band Bogoliubov-de Gennes model. We show the presence of discrepant correlation lengths leading to vortex clustering in two-band superconductors.

The phase diagrams and the nature of the phase transitions in multicomponent gauge theories with an Abelian gauge field are important topics with various physical applications. While an early renormalization-group-based study indicated that the direct transition from a fully ordered to a fully disordered state is continuous for N=1 and N>183, recently it was demonstrated that the transition is discontinuous for N=2. We quantitatively study the dependence on N of the degree of discontinuity of this transition. Our results suggest that the transition is discontinuous at least up to N=7. Furthermore, we demonstrate that, at increased coupling strength, the phase transitions of the neutral and charged sectors of the model split, which for N>2 yields a new phase with composite order. The transition from the composite-order phase to the fully disordered phase is then also discontinuous, at least for N=3 and N=4. Via a duality argument, this indicates that van der Waals-type interaction between directed loops may be responsible for the discontinuous phase transitions in these models.

This is an Editorial for the Special Issue on Solitons in Quantum Physics.

We introduce the concept of composite topological order in multicomponent systems. In such a state topological order appears only in higher-than-usual composites, with no topological order in elementary fields. We propose that such a state can be realized in Bose-Fermi mixtures in ultracold atoms.