Shortly after the Gorkovs microscopic derivation of Ginzburg-Landau model via a small order parameter expansion in BCS theory, the derivation was carried to next-to-leading order in that parameter and its spatial derivatives. The aim was to obtain a
generalized Ginzburg-Landau free energy that approximates the microscopic model better. We prove that the resulting extended Ginzburg-Landau functional does not support a superconducting state since it does not have any solutions in the form of free energy minima.
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 relati
ve 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.
Using the standard Bardeen-Cooper-Schrieffer (BCS) theory, we revise microscopic derivation of the superconductor-insulator boundary conditions for the Ginzburg-Landau (GL) model. We obtain a negative contribution to free energy in the form of surfac
e integral. Boundary conditions for the conventional superconductor have the form $textbf{n} cdot abla psi = text{const} psi$. These are shown to follow from considering the order parameter reflected in the boundary. The boundary conditions are also derived for more general GL models with higher-order derivatives and pair-density-wave states. It shows that the boundary states with higher critical temperature and the boundary gap enhancement, found recently in BCS theory, are also present in microscopically-derived GL theory. In the case of an applied external field, we show that the third critical magnetic-field value $H_{c3}$ is higher than what follows from the de Gennes boundary conditions and is also significant in type-I regime.
We discuss the unconventional magnetic response and vortex states arising in noncentrosymmetric superconductors with chiral octahedral and tetrahedral ($O$ or $T$) symmetry. We microscopically derive Ginzburg-Landau free energy. It is shown that due
to spin-orbit and Zeeman coupling magnetic response of the system can change very significantly with temperature. For sufficiently strong coupling this leads to a crossover from type-1 superconductivity at elevated temperature to vortex states at lower temperature. The external magnetic field decay in such superconductors does not have the simple exponential law. We show that in the London limit, magnetic field can be solved in terms of complex force-free fields $vec{W}$, which are defined by $ abla times vec{W} = text{const} vec{W}$. Using that we demonstrate that the magnetic field of a vortex decays in spirals. Because of such behavior of the magnetic field, the intervortex and vortex-boundary interaction becomes non-monotonic with multiple minima. This implies that vortices form bound states with other vortices, antivortices, and boundaries.
In this work we present a systematic study of the three-dimensional extension of the ring dark soliton examining its existence, stability, and dynamics in isotropic harmonically trapped Bose-Einstein condensates. Detuning the chemical potential from
the linear limit, the ring dark soliton becomes unstable immediately, but can be fully stabilized by an external cylindrical potential. The ring has a large number of unstable modes which are analyzed through spectral stability analysis. Furthermore, a few typical destabilization dynamical scenarios are revealed with a number of interesting vortical structures emerging such as the two or four coaxial parallel vortex rings. In the process of considering the stability of the structure, we also develop a modified version of the degenerate perturbation theory method for characterizing the spectra of the coherent structure. This semi-analytical method can be reliably applied to any soliton with a linear limit to explore its spectral properties near this limit. The good agreement of the resulting spectrum is illustrated via a comparison with the full numerical Bogolyubov-de Gennes spectrum. The application of the method to the two-component ring dark-bright soliton is also discussed.
We show that in superconductors that break time reversal symmetry and have anisotropy, such as p+ip materials, all order parameters and magnetic modes are mixed. Excitation of the gap fields produces an excitation of the magnetic field and vice versa
. Correspondingly the long-range decay of the magnetic field and order parameter are in general given by the same exponent. Thus one cannot characterize p+ip superconductors by the usual coherence and magnetic field penetration lengths. Instead the system has normal modes that are associated with linear combinations of magnetic fields, moduli of and phases of the order parameter components. Each such normal mode has its own decay length that plays the role of a hybridized coherence/magnetic field penetration length. On a large part of the parameter space these exponents are complex. Therefore the system in general has damped oscillatory decay of the magnetic field accompanied by damped oscillatory variation of the order parameter fields.
Bardeen-Cooper-Schrieffer (BCS) theory describes a superconducting transition as a single critical point where the gap function or, equivalently, the order parameter vanishes uniformly in the entire system. We demonstrate that in superconductors desc
ribed by standard BCS models, the superconducting gap survives near the sample boundaries at higher temperatures than superconductivity in the bulk. Therefore, conventional superconductors have multiple critical points associated with separate phase transitions at the boundary and in the bulk. We show this by revising the Caroli-De Gennes-Matricon theory of a superconductor-vacuum boundary and finding inhomogeneous solutions of the BCS gap equation near the boundary, which asymptotically decay in the bulk. This is demonstrated for a BCS model of almost free fermions and for lattice fermions in a tight-binding approximation. The analytical results are confirmed by numerical solutions of the microscopic model. The existence of these boundary states can manifest itself as discrepancies between the critical temperatures observed in calorimetry and transport probes.
Cooper-pair formation in a system of imbalanced fermions leads to the well-studied Fulde-Ferrell or Larkin-Ovchinnikov superfluid state. In the former case the system forms spontaneous phase gradients while in the latter case it forms a stripelike or
a crystal-like density gradient. We show that in multicomponent imbalanced mixtures, the superfluid states can be very different from the Fulde-Ferrell-Larkin-Ovchinnikov states. The system generates gradients in both densities and phases by forming three-dimensional vortex-antivortex lattices or lattices of linked vortex loops. The solutions share some properties with the ostensibly unrelated Skyrme model of densely packed baryons and can be viewed as synthetic realization of nuclear Skyrme matter.
Larkin-Ovchinnikov superconducting state has spontaneous modulation of Cooper pair density, while Fulde-Ferrell state has a spontaneous modulation in the phase of the order parameter. We report that a quasi-two-dimensional Dirac metal, under certain
conditions has principally different inhomogeneous superconducting states that by contrast have spontaneous modulation in a submanifold of a multiple-symmetries-breaking order parameter. The first state we find can be viewed as a nematic superconductor where the nematicity vector spontaneously breaks rotational and translational symmetries due to spatial modulation. The other demonstrated state is a chiral superconductor with spontaneously broken time-reversal and translational symmetries. It is characterized by an order parameter, which forms a lattice pattern of alternating chiralities.
Fulde, Ferrell, Larkin, and Ovchinnikov (FFLO) predicted inhomogeneous superconducting and superfluid ground states, spontaneously breaking translation symmetries. In this Letter, we demonstrate that the transition from the FFLO to the normal state a
s a function of temperature or increased Fermi surface splitting is not a direct one. Instead the system has an additional phase transition to a different state where pair-density-wave superconductivity (or superfluidity) exists only on the boundaries of the system, while the bulk of the system is normal. The surface pair-density-wave state is very robust and exists for much larger fields and temperatures than the FFLO state.
