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The iron-based superconductors allow for a zoo of possible order parameters due to their orbital degrees of freedom. These order parameters are often written in an orbital basis for a microscopic analysis and a comprehensive symmetry classification. Unlike in standard single-band superconductors, where electrons of the same band--and hence, energy--are paired, a general order parameter in such a multi-orbital system also contains pairing of electrons belonging to different bands. As this corresponds to pairing of electrons of different energy, such order parameters are energetically less stable. Here, we present a simple criterion for a stability analysis of the orbital part of the gap function based on the basic principle that electrons of equal energy are paired in the superconducting state. This not only allows us to find the most stable states, but also to identify the terms in a (tight-binding) Hamiltonian suppressing any given superconducting state. Our approach thus allows us to identify the minimal Hamiltonian necessary to compare competing instabilities. [ABSTRACT FROM AUTHOR]

A major question in Fe-based superconductors remains the structure of the pairing, in particular whether it is of unconventional nature. The electronic structure near a vortex can serve as a platform for phase-sensitive measurements to answer this question. By solving the Bogoliubov-de Gennes equations for LiFeAs, we calculate the energy-dependent local electronic structure near a vortex for different nodeless gap-structure possibilities. At low energies, the local density of states (LDOS) around a vortex is determined by the normalstate electronic structure. At energies closer to the gap value, however, the LDOS can distinguish an anisotropic s-wave gap from a conventional isotropic s-wave gap.We show within our self-consistent calculation that in addition, the local gap profile differs between a conventional and an unconventional pairing.We explain this through admixing of a secondary order parameter within Ginzburg-Landau theory. In-field scanning tunneling spectroscopy near a vortex can therefore be used as a real-space probe of the gap structure. [ABSTRACT FROM AUTHOR]

We discuss possible pairing symmetries in the hexagonal pnictide superconductor SrPtAs. The local lack of inversion symmetry of the two distinct conducting layers in the unit cell results in a special spin-orbit coupling with a staggered structure. We classify the pairing symmetry by the global crystal point group D3d, and suggest some candidates for the stable state using a tight-binding model with an in-plane, density-density type pairing interaction. We may have some unconventional states such as s + f wave and a mixture of chiral d wave and chiral p wave. The spin-orbit coupling is larger than the interlayer hopping, and the mixing between spin-singlet and spin-triplet states can be seen in spite of the fact that the system has a global inversion center. [ABSTRACT FROM AUTHOR]

Symmetry of the crystal lattice can be a determining factor for the structure of Cooper pairs in unconventional superconductors. In this study we extend the discussion of superconductivity in noncentrosymmetric materials to the case when inversion symmetry is missing locally, but is present on a global level. Concretely, we investigate the staggered noncentrosymmetricity within a regular sublattice structure, in some analogy to the discussion of superconductivity in antiferromagnetic systems. Three crystal structures are analyzed in detail as illustrative examples for the extended classification of Cooper-pairing channels. One of the cases may be relevant for the class of iron-pnictide superconductors. [ABSTRACT FROM AUTHOR]

Motivated by recent experiments on high-Tc cuprate superconductors pointing toward intra-unit-cell (IUC) order in the pseudogap phase, we investigate three distinct intra-unit-cell-ordering possibilities: nematic, nematic-spin- nematic, and current-loop order. The first two are Fermi-surface instabilities involving a spontaneous charge and magnetization imbalance between the two oxygen sites in the unit cell, respectively, while the third describes circulating currents within the unit cell. We analyze the three-band Emery model of a single CuO2 layer including various on-site and nearest-neighbor interactions within a self-consistent mean-field approach. We show how these on-site and further-neighbor repulsions suppress or enhance particular IUC orders. In particular, we show that the attractive interactions necessary for nematic and nematic-spin-nematic orders in one-band models have their natural microscopic origin in the O-O on-site and nearest-neighbor repulsions in the three-band model. Finally, we find that while the nematic and nematic-spin-nematic orders cannot coexist in this framework, the loop-current order can coexist with nematic order. [ABSTRACT FROM AUTHOR]

For a tetragonal material, order parameters of px and py symmetry are related by rotation and hence have the same Tc at a mean-field level. This degeneracy can be lifted by a symmetry-breaking field, such as (uniaxial) in-plane strain, such that at Tc, the order parameter is only of px or py symmetry. Only at a lower temperature also the respective other order parameter condenses to form a chiral p-wave state. At the mean-field level, the derivative of Tc with strain is discontinuous at zero strain. We analyze the consequences of (thermal) fluctuations on the strain-temperature phase diagram within a Ginzburg-Landau approach. We find that the order-parameter fluctuations can drive the transition to be weakly first order, rounding off this discontinuity. We discuss the possibility of a second-order transition into a nonsuperconducting time-reversal-symmetry-breaking phase and consequences for the spin-triplet superconductor Sr2RuO4. [ABSTRACT FROM AUTHOR]

Much interest in the superconducting proximity effect in three-dimensional (3D) topological insulators (TIs) has been driven by the potential to induce Majorana bound states at the interface. Most candidate materials for 3D TI, however, are bulk metals, with bulk states at the Fermi level coexisting with well-defined surface states exhibiting spin-momentum locking. In such topological metals, the proximity effect can differ qualitatively from that in TIs. By studying a model topological metal-superconductor (TM-SC) heterostructure within the Bogoliubov-de Gennes formalism, we show that the pair amplitude reaches the naked surface, unlike in a topological insulator-superconductor (TI-SC) heterostructure where it is confined to the interface. Furthermore, we predict vortex-bound-state spectra to contain a Majorana zero mode localized at the naked surface, separated from the bulk vortex-bound-state spectra by a finite energy gap in such a TM-SC heterostructure. These nakedsurface- bound modes are amenable to experimental observation and manipulation, presenting advantages of TM-SC over TI-SC. [ABSTRACT FROM AUTHOR]

The modern understanding of topological insulators is based on Wannier obstructions in position space. Motivated by this insight, we study topological superconductors from a position-space perspective. For a one-dimensional superconductor, we show that the wave function of an individual Cooper pair decays exponentially with separation in the trivial phase and polynomially in the topological phase. For the position-space Majorana representation, we show that the topological phase is characterized by a nonzero Majorana polarization, which captures an irremovable and quantized separation of Majorana Wannier centers from the atomic positions. We apply our results to diagnose second-order topological superconducting phases in two dimensions. Our work establishes a vantage point for the generalization of topological quantum chemistry to superconductivity. [ABSTRACT FROM AUTHOR]

The recent discovery of AV3Sb5 (A=K,Rb,Cs) has uncovered an intriguing arena for exotic Fermi surface instabilities in a kagome metal. Among them, superconductivity is found in the vicinity of multiple van Hove singularities, exhibiting indications of unconventional pairing. We show that the sublattice interference mechanism is central to understanding the formation of superconductivity in a kagome metal. Starting from an appropriately chosen minimal tight-binding model with multiple van Hove singularities close to the Fermi level for AV3Sb5, we provide a random phase approximation analysis of superconducting instabilities. Nonlocal Coulomb repulsion, the sublattice profile of the van Hove bands, and the interaction strength turn out to be the crucial parameters to determine the preferred pairing symmetry. Implications for potentially topological surface states are discussed, along with a proposal for additional measurements to pin down the nature of superconductivity in AV3Sb5. [ABSTRACT FROM AUTHOR]