Pairing symmetry and pairing state in ferropnictides: Theoretical overview

We review the main ingredients for an unconventional pairing state in the ferropnictides, with particular emphasis on interband pairing due to magnetic fluctuations. Summarizing the key experimental prerequisites for such pairing, the electronic structure and nature of magnetic excitations, we discuss the properties of the s^± state that emerges as a likely candidate pairing state for these materials and survey experimental evidence in favor of and against this novel state of matter.     

Class of exactly solvable pairing models

We present three classes of exactly solvable models for fermion and boson systems, based on the pairing interaction. These models are solvable in any dimension. As an example we show the first results for fermions interacting with repulsive pairing forces in a two-dimensional square lattice. In spite of the repulsive pairing force the exact results show attractive pair correlations.     

Nodal d + id pairing and topological phases on the triangular lattice of Na(x)CoO(2).yH(2)O: evidence for an unconventional superconducting state

We show that finite angular momentum pairing chiral superconductors on the triangular lattice have point zeroes in the complex gap function. A topological quantum phase transition takes place through a nodal superconducting state at a specific carrier density x(c) where the normal state Fermi surface crosses the isolated zeros. For spin-singlet pairing, we show that the second-nearest-neighbor (d+id)-wave pairing can be the dominant pairing channel. The gapless critical state at x (c) approximately 0.25 has six Dirac points and is topologically nontrivial with a T3 spin relaxation rate below T(c). This picture provides a possible explanation for the unconventional superconducting state of Na(x)Co O(2). yH(2)O. Analyzing a pairing model with strong correlation using the Gutzwiller projection and symmetry arguments, we study these topological phases and phase transitions as a function of Na doping.     

Electron-hole symmetry and solutions of Richardson pairing model

Richardson approach provides an exact solution of the pairing Hamiltonian. This Hamiltonian is characterized by the electron-hole pairing symmetry, which is however hidden in Richardson equations. By analyzing this symmetry and using an additional conjecture, fulfilled in solvable limits, we suggest a simple expression of the ground state energy for an equally-spaced energy-level model, which is applicable along the whole crossover from the superconducting state to the pairing fluctuation regime. Solving Richardson equations numerically, we demonstrate a good accuracy of our expression.     

Collective pairing Hamiltonian in the GCM approximation

Using the generator coordinate method and the gaussian overlap approximation we derived the collective Schrödinger-type equation starting from a microscopic single-particle plus pairing hamiltonian for one kind of particle. The BCS wave function was used as the generator function. The pairing energy-gap parameter Δ and the gauge transformation angle ø were taken as the generator coordinates. Numerical results have been obtained for the full and the mean-field pairing hamiltonians and compared with the cranking estimates. A significant role played by the zero-point energy correction in the collective pairing potential is found. The ground-state energy dependence on the pairing strength agrees very well with the exact solution of the Richardson model for a set of equidistant doubly-degenerate single-particle levels.     

Phase-sensitive tests of the pairing state symmetry in Sr(2)RuO(4)

Exotic superconducting properties of have provided strong support for an unconventional pairing symmetry. However, the extensive efforts over the past decade have not yet unambiguously resolved the controversy about the pairing symmetry in this material. While recent phase-sensitive experiments using flux modulation in Josephson junctions consisting of and a conventional superconductor have been interpreted as conclusive evidence for a chiral spin-triplet pairing, we propose here an alternative interpretation. We show that an overlooked chiral spin-singlet pairing is also compatible with the observed phase shifts in Josephson junctions and propose further experiments which would distinguish it from its spin-triplet counterpart.     

Pairing in doped inversion-symmetric Weyl semimetals: a finite temperature analysis from Thouless criterion

In doped Weyl semimetal with inversion symmetry, the two pairing states, i.e., the zero momentum BCS pairing and the finite momentum Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing are possible in principle. In this paper we use the standard Thouless criterion for the onset of pairings to investigate the leading pairing instability at the finite temperature. Our results suggest that both BCS and FFLO instabilities are possible depending on the on-site attractive interaction. The competition between the BCS pairing and FFLO pairing is driven by the mutual suppression between density of state near the Fermi surface and finite energy band structure in the whole Brillouin zone. For small and intermediate interaction, the former dominates and supports BCS pairing, while for strong interaction, the latter wins and favors FFLO pairing. We expect our results at the finite temperature can provide some important message to identify the true ground state.     

Pairing in spin polarized two-species fermionic mixtures with mass asymmetry

We discuss on the pairing mechanism of fermions with mismatch in their Fermi momenta due to a mass asymmetry. Using a variational ansatz for the ground state we also discuss the BCS-BEC crossover of this system. It is shown that the breached pairing solution with a single Fermi surface is stable in the BEC regime. We also include the temperatures effect on the fermion pairing within an approximation that is valid for temperatures much below the critical temperature.     

Tunneling Conductance in a Normal Metal/Ferromagnetic Superconductor Nano-Junction at a Finite Temperature

In this study, we investigate the tunneling conductance at a finite temperature in a normal metal/ferromagnetic superconductor nano-junction where the ferromagnetic superconductor (FS) is in three different cooper pairing states: spin singlet s-wave pairing (SWP), spin triplet opposite spin pairing (OSP), and spin triplet equal spin pairing (ESP) while including Fermiwave mismatch (FWM) and effective mass mismatch (EMM) in two sides of the nano-junction. We find that the conductance shows clearly different behaviors all depending on the symmetries of cooper pairing in a mannerthat the conductance spectra shows a gap-like structure, two interior dipsstructure and zero bias peak for SWP, OSP, and ESP, respectively. Also, theeffective FS gap (δ_eff) is a linear and decreasing function of exchange field. The slope of (δ_eff) versus exchange field for OSP is twice the SWP. Thus, we can determine the spin polarization of N/FS nano-junction based on the dependence of (δ_eff) to exchange field.     

Theory of oxide high temperature superconductivity

We propose a model Hamiltonian for the high temperature superconductivity from the analogy of the BCS model hamiltonian. We seek a possibility of real space electron pairing. It follows then the magnetic exchange interaction is not a source of pairing and we propose a form of pairing interaction from the argument of the broken symmetry of electron number conservation. Based on a variational wave function, the ground state energy of our model is studied.     

Chiral p-wave pairing of ultracold fermionic atoms due to a quadratic band touching

We study the superfuild ground state of ultracold fermions in optical lattices with a quadratic band touching. Examples are a checkerboard lattice around half filling and a kagome lattice above one third filling. Instead of pairing between spin states, here we focus on pairing interactions between different orbital states. We find that our systems have only odd-parity(orbital) pairing instability while the singlet(orbital) pairing instability vanishes thanks to the quadratic band touching. In the mean field level, the ground state is found to be a chiral p-wave pairing superfluid(mixed with finite f-wave pairing order-parameters) which supports Majorana fermions.     

Dynamics of the pairing interaction in the hubbard and t-J models of high-temperature superconductors

The question of whether one should speak of a "pairing glue" in the Hubbard and t-J models is basically a question about the dynamics of the pairing interaction. If the dynamics of the pairing interaction arises from virtual states, whose energies correspond to the Mott gap, and give rise to the exchange coupling J, the interaction is instantaneous on the relative time scales of interest. In this case, while one might speak of an "instantaneous glue," this interaction differs from the traditional picture of a retarded pairing interaction. However, as we will show, the dominant contribution to the pairing interaction for both of these models arises from energies reflecting the spectrum seen in the dynamic spin susceptibility. In this case, the basic interaction is retarded, and one speaks of a spin-fluctuation glue which mediates the d-wave pairing.     

Density-matrix renormalization group study of pairing when electron-electron and electron-phonon interactions coexist: effect of the electronic band structure

The density-matrix renormalization group is used to study the pairing when both electron-electron and electron-phonon interactions are strong in the Holstein-Hubbard model at half filling in a region intermediate between the adiabatic (Migdal's) and antiadiabatic limits. We have found (i) the pairing correlation obtained for a one-dimensional system is nearly degenerate with the charge density-wave correlation in a region where the phonon-induced attraction is comparable with the electron-electron repulsion, but (ii) pairing becomes dominant when we destroy the electron-hole symmetry in a trestle lattice. This provides an instance in which pairing can arise, in a lattice-structure dependent manner, from coexisting electron-electron and electron-phonon interactions.     

Josephson current versus potential strength of the interface in ferromagnetic superconductors

Based on the scattering theory, we calculate the Josephson current in a junction between two ferromagnetic superconductors as a function of the interface potential z. We consider the ferromagnetic superconductor(FS) in three different Cooper pairing states: spin singlet s-wave pairing(SWP) state, spin triplet opposite spin pairing(OSP) state, and spin triplet equal spin pairing(ESP) state. We find that the critical Josephson current as a function of z shows clear differences among the SWP, OSP, and ESP states. The obtained results can be used as a useful tool for determining the pair symmetry of the ferromagnetic superconductors.     

Dirac fermions and conductance oscillations in s- and d-wave superconductor-graphene junctions

We investigate quantum transport in a normal-superconductor graphene heterostructure, including the possibility of an anisotropic pairing potential in the superconducting region. We find that under certain circumstances, the conductance displays an undamped, oscillatory behavior as a function of applied bias voltage. Also, we investigate how the conductance spectra are affected by a d-wave pairing symmetry. These results combine unusual features of the electronic structure of graphene with the unconventional pairing symmetry found for instance in high-Tc superconductors.     

Angular momentum mixing in single flavor color superconductivity with transverse pairing

Because of the equal strength of the pairing potential mediated by one-gluon exchange for all partial waves to the leading order QCD running coupling constant and the nonlinearity of the gap equation, the non-spherical pairing in single flavor color superconductivity (CSC) cannot be restricted in a single non-s-wave channel and the mixing among different angular momenta will occur. In this paper, we examine the angular momentum mixing in single flavor CSC of massless quarks with transverse pairing, in which the pairing quarks have opposite helicity. We find that the free energy of all non-spherical pairing states are lowered by angular momentum mixing compared with that contain p-wave only, though the amount of the free energy drop is numerically small. Consequently the most stable pairing state in the ultra-relativistic limit remains the spherical color-spin-locked state (CSL).     

Multi-band pairing of ultrarelativistic electrons and holes in graphene bilayer

Multi-band pairing of effectively ultrarelativistic electrons and holes in asymmetrically biased graphene bilayer in strong coupling regime is considered. In this regime, the pairing affects both conduction and valence bands of the both graphene layers, and the order parameter is a matrix, which indices correspond to the bands. For band-diagonal s-wave pairing, we derive the system of multi-band gap equations for the gaps in the valence and conduction bands and solve it in the approximation of constant gaps and in the approximation of separable pairing potential. For a characteristic width of the pairing region of order of magnitude of the chemical potential, the gap values are not much different from single-band BCS estimations. However, if the pairing region is wider, then the gaps can be much larger and depend exponentially on its energy width. We also predict gapped and soliton-like oscillations of a relative phase of the gaps and unpairing of quarter-vortices at Kosterlitz-Thouless transition.     

Superfluid pairing gap in strong coupling

The zero-temperature pairing gap is a fundamental property of interacting Fermions, providing a crucial test of many-body theories in strong coupling. We analyze recent cold-atom experiments on imbalanced Fermi systems using Quantum Monte Carlo results for the superfluid and normal phases. Through this analysis we extract, for the first time, the experimental zero-temperature pairing gap in the fully paired superfluid state at unitarity where the two-body scattering length is infinite. We find that the zero-temperature pairing gap is greater than 0.4 times the Fermi energy E(F), with a preferred value of (0.45+/-0.05) E(F). The ratio of the pairing gap to the Fermi Energy is larger here than in any other Fermi system measured to date.     

Calculation of the nuclear inertia in a generalized cranking model

By use of a time-dependent formalism, we generalize the Inglis cranking model to include the velocity dependence of the single-particle potential and the reaction of the pairing field to the collective motion. This generalized cranking model is used to calculate the inertia for spheroidal deformations of²⁴⁰Pu in both a pure harmonicoscillator potential and a harmonic-oscillator potential with spin-orbit interaction. For comparisons with irrotational values, we transform to the inertia with respect to a matter coordinate that specifies the distance between the centers of mass of the two halves of the nucleus. We study in particular the dependence of the inertia upon nuclear temperature in the absence of pairing, and its dependence upon pairing strength for zero temperature.     

Synchronization in the BCS pairing dynamics as a critical phenomenon

Fermi gas with time-dependent pairing interaction hosts several different dynamical states. Coupling between the collective BCS pairing mode and individual Cooper pair states can make the latter either synchronize or dephase. We describe transition from phase-locked undamped oscillations to Landau-damped dephased oscillations in the collisionless, dissipationless regime as a function of coupling strength. In the dephased regime, we find a second transition at which the long-time asymptotic pairing amplitude vanishes. Using a combination of numerical and analytical methods we establish a continuous (type II) character of both transitions.