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The magnetization process of a superconductor is determined by the potential barrier for vortex nucleation and escape. In multicomponent superconductors, fractional vortices with a winding in the phase of only one of the components can be stable topological solitons that carry a fraction of the flux quantum. While the formation of such objects in the bulk costs logarithmically or linearly divergent energy, these objects were shown to be stable near samples' boundaries in the two-component London model. Therefore, the conventional Bean-Livingston picture of magnetic flux entry does not apply to these superconductors, since the entry process can involve fractionalization of a vortex. In this paper, we address the nonlinear problem of determining the potential barrier for fluxoid penetration in a multicomponent superconductor, including the effects of various intercomponent couplings, by using the recently developed gauged string method. The method allows numerically exact (i.e., convergent) calculation of a sphaleron configuration in a gauge theory and thus the height of the nucleation barrier. We show how the fractionalized nucleation processes result in multiple sphalerons and intermediate states due to the complex shape of the energy landscape of multicomponent superconductors., Comment: 11 pages, 13 figures

We consider the interface between a Bardeen-Cooper-Schrieffer superconductor and non-superconducting band insulator. We show that under certain conditions, such interfaces can have an elevated superconducting critical temperature, without increasing the strength of the pairing interaction at the interface. We identify the regimes where the interface critical temperature exceeds the critical temperature associated with a superconductor-vacuum interface., Comment: Version published in Physical Review B. Two-dimensional solutions added

The recent Comment by Vorontsov [arXiv:2007.13696] claims that surface pair-density-wave superconductivity with critical temperature higher than the bulk FFLO critical temperature is not supported by microscopic theory. The conclusion is reached by using an approximate semi-microscopic quasiclassical approach. Here we show that a fully microscopic approach unambiguously demonstrates the existence of surface pair-density-wave superconductivity.

We present a microscopic study of the behavior of the order parameters near boundaries of a two-band superconducting material, described by the standard tight-binding Bardeen-Cooper-Schrieffer model. We find superconducting surface states. The relative difference between bulk and surface critical temperatures is a nontrivial function of the interband coupling strength. For superconductors with weak interband coupling, boundaries induce variations of the gaps with the presence of multiple length scales, despite non-zero interband Josephson coupling., 7 pages, 7 figures

The knowledge of vortex nucleation barriers is crucial for applications of superconductors, such as single-photon detectors and superconductor-based qubits. Contrarily to the problem of finding energy minima and critical fields, there are no controllable methods to explore the energy landscape, identify saddle points, and compute associated barriers. Similar problems exist in high-energy physics where the saddle-point configurations are called sphalerons. Here, we present a generalization of the string method to gauge field theories, which allows the calculation of energy barriers in superconductors. We solve the problem of vortex nucleation, assessing the effects of the nonlinearity of the model, complicated geometry, surface roughness, and pinning., 12 pages, 14 figures

One of the defining features of spontaneously broken time-reversal symmetry (BTRS) is the existence of domain walls, the detection of which would be strong evidence for such systems. There is keen interest in BTRS currently, in part, due to recent muon spin rotation experiments, which have pointed towards Ba1−x Kx Fe2 As2 exhibiting a remarkable case of s-wave superconductivity with spontaneously broken time-reversal symmetry. A key question, however, is how to differentiate between the different theoretical models which describe such a state. Two particularly popular choices of model are s + is and s + id superconducting states. In this paper, we obtain solutions for domain walls in s + is and s + id systems, including the effects of lattice anisotropies. We show that, in general, both models exhibit spontaneous magnetic fields that extend along the entire length of the domain wall. We demonstrate the qualitative difference between the magnetic signatures of s + is and s + id domain walls and propose a procedure to extract the superconducting pairing symmetry from the magnetic-field response of domain walls.

We describe boundary effects in superconducting systems with Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting instability, using Bogoliubov-de-Gennes and Ginzburg-Landau (GL) formalisms. First, we show that in dimensions larger than one the standard GL functional formalism for FFLO superconductors is unbounded from below. This is demonstrated by finding solutions with zero Laplacian terms near boundaries. We generalize the GL formalism for these systems by retaining higher order terms. Next, we demonstrate that a cuboid sample of a superconductor with imbalanced fermions at a mean-field level has a sequence of the phase transitions. At low temperatures it forms Larkin-Ovchinnikov state in the bulk but has a different modulation pattern close to the boundaries. When temperature is increased the first phase transition occurs when the bulk of the material becomes normal while the faces remain superconducting. The second transition occurs at higher temperature where the system retains superconductivity on the edges. The third transition is associated with the loss of edge superconductivity while retaining superconducting gap in the vertices. We obtain the same sequence of phase transition by numerically solving the Bogoliubov-de Gennes model., published version