We consider the superfluid density ρs(T ) in a two-band superconductor with sign-changing extended s-wave symmetry (s + ) in the presence of non-magnetic impurities and apply the results to Fe-pnictides. We show that the behavior of the superfluid density is essentially the same as in an ordinary s-wave superconductor with magnetic impurities. We show that, for moderate to strong inter-band impurity scattering, ρs(T ) behaves as a power-law T n with n ≈ 1.6 ÷ 2 over a wide range of T . We argue that the power-law behavior is consistent with recent experiments on the penetration depth λ(T ) in doped BaFe2As2, but disagree quantitatively with the data on LaFePO.

We present a detailed description of two-band quasi-two-dimensional metals with s-wave superconducting ͑SC͒ and antiferromagnetic spin-density-wave ͑SDW͒ correlations. We present a general approach and use it to investigate the influence of the difference between the shapes and the areas of the two Fermi surfaces on the phase diagram. In particular, we determine the conditions for the coexistence of SC and SDW orders at different temperatures and dopings. We argue that a conventional s-wave SC order coexists with SDW order only at very low T and in a very tiny range of parameters. An extended s-wave superconductivity, for which SC gap changes sign between the two bands, coexists with antiferromagnetic SDW over a much wider range of parameters and temperatures but even for this SC order the regions of SDW and SC can still be separated by a first-order transition. We show that the coexistence range becomes larger if SDW order is incommensurate. We apply our results to iron-based pnictide materials, in some of which coexistence of SDW and SC orders has been detected.

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We investigate the ground state properties of a noncentrosymmetric superconductor near a surface. We determine the spectrum of Andreev bound states due to surface-induced mixing of bands with opposite spin helicities for a Rashba-type spin-orbit coupling. We find that the order parameter suppression qualitatively changes the bound state spectrum. The spin structure of Andreev states leads to a spin supercurrent along the interface, which is strongly enhanced compared to the normal state spin current. Particle and hole coherence amplitudes show Faraday-like rotations of the spin along quasiparticle trajectories.

Using general symmetry arguments and model calculations we analyze the superconducting gap in materials with multiple Fermi-surface pockets, with applications to iron pnictides. We show that the gap in the pnictides has an extended s-wave symmetry but is either nodeless or has nodes, depending on the interplay between intraband and interband interactions. We argue that the nodes in the gap emerge without a phase transition as the tendency toward a spin-density-wave order gets weaker. These findings provide a way to reconcile seemingly conflicting results of numerical and experimental studies of the pnictides.

We consider a quasi-two-dimensional superconductor with line nodes in the presence of an in-plane magnetic field, and compute the dependence of the specific heat C and the in-plane heat conductivity kappa on the angle between the field and the nodal direction in the vortex state. We use a variation of the microscopic Brandt-Pesch-Tewordt method that accounts for the scattering of quasiparticles off vortices, and analyze the signature of the nodes in C and kappa. At low to moderate fields the specific heat anisotropy changes sign with increasing temperature. Comparison with measurements of C and kappa in CeCoIn(5) resolves the contradiction between the two in favor of the d((x(2)-y(2)) gap.

We develop a fully microscopic theory for the calculations of the angle-dependent properties of unconventional superconductors under a rotated magnetic field. We employ the quasiclassical Eilenberger equations, and use a variation of the Brandt-Pesch-Tewordt (BPT) method to obtain a closed form solution for the Green's function. The equations are solved self-consistently for quasitwo-dimensional d x 2 −y 2 (dxy) superconductors with the field rotated in the basal plane. The solution is used to determine the density of states and the specific heat. We find that applying the field along the gap nodes may result in minima or maxima in the angle-dependent specific heat, depending on the location in the T -H plane. This variation is attributed to the scattering of the quasiparticles on vortices, which depends on both the field and the quasiparticle energy, and is beyond the reach of the semiclassical approximation. We investigate the anisotropy across the T -H phase diagram, and compare our results with the experiments on heavy fermion CeCoIn5.

We present NMR data in the normal and superconducting states of CeCoIn5 for fields close to Hc2(0)= 11.8 T in the ab plane. Recent experiments identified a first-order transition from the normal to superconducting state for H > 10.5 T, and a new thermodynamic phase below 290 mK within the superconducting state. We find that the Knight shifts of the In(1), In(2) and the Co are discontinuous across the first-order transition and the magnetic linewidths increase dramatically. The broadening differs for the three sites, unlike the expectation for an Abrikosov vortex lattice, and suggests the presence of static spin moments in the vortex cores. In the low-temperature and highfield phase the broad NMR lineshapes suggest ordered local moments, rather than a long wavelength quasiparticle spin density modulation expected for an FFLO phase.PACS numbers: 71.27.+a, 74.70.Tx, 75.20.Hr One of the most intriguing properties observed in Kondo lattice systems is the emergence of unconventional superconductivity near a quantum critical point (QCP). By varying some external parameter such as field or pressure, an antiferromagnetic ground state can be tuned such that the transition temperature goes to zero at the QCP. As the tuning parameter increases past the QCP, conventional Fermi-liquid behavior is recovered below a characteristic temperature T FL [1]. Superconductivity often emerges as the ground state of the system for sufficiently low temperatures in the vicinity of the QCP [2]. The heavy-fermion superconductor CeCoIn 5 exhibits many properties typical of a Kondo lattice system at a QCP. In particular, T FL appears to vanish at the superconducting critical field H c2 (T = 0) for fields along the c axis, suggesting the presence of a field-tuned QCP [3,4]. This interpretation has remained contentious because the ordered state associated with the QCP is superconductivity rather than antiferromagnetism. One explanation is that an antiferromagnetic (AFM) phase is hidden within the superconducting phase diagram, which is the genitor of both the QCP and non-Fermi liquid behavior in the vicinity of H c2 (0). However, when the superconductivity is suppressed with Sn doping, the QCP tracks H c2 (0), and no magnetic state emerges in the phase diagram, whereas pressure separates the QCP [5].In fact, there is a field-induced state, which we will refer to as the B phase, in the H − T phase diagram of CeCoIn 5 that exists just below H c2 (0). The order parameter of the B phase could be either (1) a different symmetry of the superconducting order parameter, (2) a fieldinduced magnetic phase, or (3) a Fulde-Ferrell-LarkinOvchinnikov (FFLO) superconducting phase [6,7,8,9]. The normal to superconducting transition in this system has a critical point at (H, T ) ∼ (10.5T, 0.75K), separating a second to first order transition, and the B phase exists below a temperature T 0 (H) ∼ 290 mK and is bounded by T c (H). NMR experiments suggest the presence of excess quasiparticles associated with nodes in the superconducting FFLO wavefunction [10,11,1...