Even parity, orbital singlet, and spin triplet pairing for superconducting LaFeAsO1-xFx

Point contact Andreev reflection studies of a non-centro symmetric superconductor Re6Zr

Re₆Zr, a non-centrosymmetric superconductor is an interesting system as recent experimental evidence suggests that the superconducting state breaks time reversal symmetry. This implies a mixing of spin singlet-triplet states leading to a complex order parameter in this system. Here, we report point contact Andreev Reflection (PCAR) measurements on a single crystal of Re₆Zr (superconducting transition temperature (T_c) = 6.78 K). We observe multiple gap features in the PCAR spectra which depends on the type of tip and contact. Spectral features appear at voltages 1.0 ± 0.1 mV, 0.75 ± 0.05 mV and 0.45 ± 0.1 mV suggesting that there are at least more than one band contributing to superconductivity. However, strong surface inter-band scattering is possibly responsible for the uncertainty in observing them together distinctly in a single contact in the PCAR measurements. Interestingly, the bulk gap (Δ  = 1.95k_BT_c = 1.1 meV) is occasionally observed in PCAR spectra, mostly with ferromagnetic tips. The gap features associated with the other two smaller gaps disappear at the bulk T_c. In addition, no anisotropy in the upper critical field was observed. Our results suggest an unconventional superconducting order in this compound: Multiband singlet states dominated by inter-band pairing which break the time reversal symmetry or singlet mixed with triplet states.

Two-Gap Superconductivity in LaNiGa_{2} with Nonunitary Triplet Pairing and Even Parity Gap Symmetry

The nature of the pairing states of superconducting LaNiC_{2} and LaNiGa_{2} has to date remained a puzzling question. Broken time reversal symmetry has been observed in both compounds and a group theoretical analysis implies a nonunitary triplet pairing state. However, all the allowed nonunitary triplet states have nodal gap functions but most thermodynamic and NMR measurements indicate fully gapped superconductivity in LaNiC_{2}. Here we probe the gap symmetry of LaNiGa_{2} by measuring the London penetration depth, specific heat, and upper critical field. These measurements demonstrate two-gap nodeless superconductivity in LaNiGa_{2}, suggesting that this is a common feature of both compounds. These results allow us to propose a novel triplet superconducting state, where the pairing occurs between electrons of the same spin, but on different orbitals. In this case the superconducting wave function has a triplet spin component but isotropic even parity gap symmetry, yet the overall wave function remains antisymmetric under particle exchange. This model leads to a nodeless two-gap superconducting state which breaks time reversal symmetry, and therefore accounts well for the seemingly contradictory experimental results.

Superconductivity from Emerging Magnetic Moments

Multiorbital Hubbard models are shown to exhibit a spatially isotropic spin-triplet superconducting phase, where equal-spin electrons in different local orbitals are paired. This superconducting state is stabilized in the spin-freezing crossover regime, where local moments emerge in the metal phase, and the pairing is substantially assisted by spin anisotropy. The phase diagram features a superconducting dome below a non-Fermi-liquid metallic region and next to a magnetically ordered phase. We suggest that this type of fluctuating-moment-induced superconductivity, which is not originating from fluctuations near a quantum critical point, may be realized in spin-triplet superconductors such as strontium ruthenates and uranium compounds.

Magnetic and pairing properties of a two-orbital model for the pnictide superconductors: a quantum Monte Carlo study

Using the constrained-path Monte Carlo method, a two-orbital model for the pnictide superconductors is studied at half filling and in both the electron- and hole-doped cases. At half filling, a stable (π, 0)/(0, π) magnetic order is explicitly observed and the system tends to be in an orthomagnetic order rather than the striped antiferromagnetic order on increasing the Coulomb repulsion U. In the electron-doped case, the (π, 0)/(0, π) magnetic order is enhanced upon doping and suppressed eventually and a s(±) pairing state dominates all the possible nearest-neighbour-bond pairings. Whereas in the hole-doped case, the magnetic order is straightforwardly suppressed and two nearly degenerate A(1g) and B(1g) intraband pairings become the dominant ones.

Scanning tunneling spectroscopy of superconducting LiFeAs single crystals: evidence for two nodeless energy gaps and coupling to a bosonic mode

The superconducting compound LiFeAs is studied by scanning tunneling microscopy and spectroscopy. A gap map of the unreconstructed surface indicates a high degree of homogeneity in this system. Spectra at 2 K show two nodeless superconducting gaps with Δ(1)=5.3±0.1 meV and Δ(2)=2.5±0.2 meV. The gaps close as the temperature is increased to the bulk T(c), indicating that the surface accurately represents the bulk. A dip-hump structure is observed below T(c) with an energy scale consistent with a magnetic resonance recently reported by inelastic neutron scattering.

Interpocket pairing and gap symmetry in Fe-based superconductors with only electron pockets

We analyze the pairing symmetry in Fe-based superconductors AFe2Se2 (A=K, Rb, Cs) which contain only electron pockets. We argue that the pairing condensate in such systems contains not only intrapocket component but also interpocket component, made of fermions belonging to different electron pockets. We analyze the interplay between intrapocket and interpocket pairing, depending on the ellipticity of electron pockets and the strength of their hybridization. We show that with increasing hybridization, the system undergoes a transition from a d-wave state to an s+- state, in which the gap changes sign between hybridized pockets. This s+- state has the full gap and at the same time supports spin resonance, in agreement with the data. Near the boundary between d and s+- states, we found a long-sought s+id state which breaks time-reversal symmetry.

Isotope and multiband effects in layered superconductors

In this review we consider three classes of superconductors, namely cuprate superconductors, MgB(2) and the new Fe based superconductors. All of these three systems are layered materials and multiband compounds. Their pairing mechanisms are under discussion with the exception of MgB(2), which is widely accepted to be a 'conventional' electron-phonon interaction mediated superconductor, but extending the Bardeen-Cooper-Schrieffer (BCS) theory to account for multiband effects. Cuprates and Fe based superconductors have higher superconducting transition temperatures and more complex structures. Superconductivity is doping dependent in these material classes unlike in MgB(2) which, as a pure compound, has the highest values of T(c) and a rapid suppression of superconductivity with doping takes place. In all three material classes isotope effects have been observed, including exotic ones in the cuprates, and controversial ones in the Fe based materials. Before the area of high-temperature superconductivity, isotope effects on T(c) were the signature for phonon mediated superconductivity-even when deviations from the BCS value to smaller values were observed. Since the discovery of high T(c) materials this is no longer evident since competing mechanisms might exist and other mediating pairing interactions are discussed which are of purely electronic origin. In this work we will compare the three different material classes and especially discuss the experimentally observed isotope effects of all three systems and present a rather general analysis of them. Furthermore, we will concentrate on multiband signatures which are not generally accepted in cuprates even though they are manifest in various experiments, the evidence for those in MgB(2), and indications for them in the Fe based compounds. Mostly we will consider experimental data, but when possible also discuss theoretical models which are suited to explain the data.

Collective excitations and response functions of two-band band-singlet and spin-triplet superconductors

The two-band band-singlet and spin-triplet superconductors are studied in the framework of functional integrals with a focus on collective excitations and their influences on response functions. The long range Coulomb interaction has been included to preserve the electromagnetic U(1) gauge invariance. The U(1) phase fluctuation and the spin wave are identified as the collective excitations. The longitudinal spin response function turns out to be solely determined by quasiparticle excitation. The transverse spin response function is determined by both the quasiparticle excitation and the spin wave. The spin wave is found not to be renormalized by long range Coulomb interaction. The density response function is determined by both the quasiparticle excitation and the U(1) phase fluctuation, but in contrast to the case of spin response functions, both of them are strongly renormalized by the long range Coulomb interaction. The nondegeneracy of the band energy can affect the response functions significantly through the contribution by collective excitations.

Nonmagnetic impurity resonances as a signature of sign-reversal pairing in FeAs-based superconductors

The energy band structure of FeAs-based superconductors is fitted by a tight-binding model with two Fe ions per unit cell and two degenerate orbitals per Fe ion. Based on this, superconductivity with extended s-wave pairing symmetry of the form cosk(x)+cosk(y) is examined. The local density of states near an impurity is also investigated by using the T-matrix approach. For the nonmagnetic scattering potential, we found that there exist two major resonances inside the gap. The height of the resonance peaks depends on the strength of the impurity potential. These in-gap resonances are originated in the Andreev's bound states due to the quasiparticle scattering between the hole Fermi surfaces around Gamma point with positive order parameter and the electron Fermi surfaces around M point with negative order parameter.

The band structure and Fermi surface of (Sr(3)Sc(2)O(5))Fe(2)As(2)

Inspired by the experience in CuO-based superconductor that a larger spacing distance between CuO planes induced a higher T(C), some researchers synthesized (Sr(3)Sc(2)O(5))Fe(2)As(2) and related compounds with spacing distances between FeAs planes as large as 15 Å and expected a higher T(C). Our density functional calculations indicate that the Fermi surface of (Sr(3)Sc(2)O(5))Fe(2)As(2) is very similar to that of LaOFeAs, while the projected band structure shows some differences. From Fermi surface nesting and the calculated Lindhard response function χ(q), we predict that a spin density wave (SDW) and stripe antiferromagnetism (AF) may exist in the undoped compound and that electron or hole doping will suppress this SDW state. Similar to LaFeAsO, both the stabilization energy and the moment are very sensitive to the As atom positions. Because of the considerable similarity to LaFeAsO, (Sr(3)Sc(2)O(5))Fe(2)As(2) is expected to become a superconductor with electron or hole doping.

Superconducting pairing symmetry and energy gaps of the two-orbital t-t'-J-J' model: comparisons with the ARPES experiments in iron pnictides

Motivated by the discovery of the iron-based superconductors, we present the theoretical results on the superconducting phase diagram, the temperature-dependent Fermi surface structures in normal state and the angle-resolved photoemission spectroscopy (ARPES) character of quasiparticles of the two-orbital t-t'-J-J' model. In the reasonable physical parameter region of LaFeAsO(1-x)F(x), we find the superconducting phase is stable, and the pairing symmetry is weakly anisotropic and nodeless d(x(2)-ηy(2))+S(x(2)y(2))-wave, qualitatively in agreement with the ARPES experiments in iron pnictide superconductors. Nevertheless, the two ratios of the energy gaps to T(c) deviate from the ARPES data, suggesting that a more elaborate theoretical model is needed.

Observation of the Josephson effect in Pb/Ba1-xKxFe2As2 single crystal junctions

We have fabricated c-axis Josephson junctions on single crystals of Ba1-xKxFe2As2 by using Pb as the counterelectrode in two geometries, planar and point contact. Junctions in both geometries show resistively shunted junction I-V curves below the T{C} of the counterelectrode. Microwave induced steps were observed in the I-V curves, and the critical currents are suppressed with an in-plane magnetic field with well-defined modulation periods indicating that the Josephson current is flowing in a manner consistent with the small to intermediate sized junction limit. I{C}R{N} products of up to 0.3 mV have been observed in these junctions at 4.2 K. The observation of Josephson coupling along the c axis between Ba1-xKxFe2As2 and a conventional superconductor suggests the existence of an s-wave symmetry in this class of iron pnictide superconductors.

Strong coupling theory for superconducting iron pnictides

Superconductivity in iron pnictides is studied by using a two-orbital Hubbard model in the large U limit. The Coulomb repulsion induces an orbital-dependent pairing between charge carriers. The pairing is found mainly from the scattering within the same Fermi pocket. The interpocket pair scatterings determine the symmetry of the superconductivity, which is extended s wave at small Hund's coupling, and d wave at large Hund's coupling and large U. The former is consistent with recent experiments of angle-resolved photoemission spectroscopy and Andreev reflection spectroscopy.

Functional renormalization-group study of the pairing symmetry and pairing mechanism of the FeAs-based high-temperature superconductor

We apply the fermion functional renormalization-group method to determine the pairing symmetry and pairing mechanism of the FeAs-Based materials. Within a five band model with pure repulsive interactions, we find an electronic-driven superconducting pairing instability. For the doping and interaction parameters we have examined, extended s wave, whose order parameter takes on opposite sign on the electron and hole pockets, is always the most favorable pairing symmetry. The pairing mechanism is the inter-Fermi-surface Josephson scattering generated by the antiferromagnetic correlation.

Optical study of LaO0.9F0.1FeAs: evidence for a weakly coupled superconducting state

We have studied the reflectance of the recently discovered superconductor LaO0.9F0.1FeAs in a wide energy range from the far infrared to the visible regime. We report on the observation of infrared active phonons, the plasma edge, and possible interband transitions. On the basis of this data and the reported in-plane penetration depth lambda{L}(0)=254 nm [H. Luetkens, Phys. Rev. Lett. 101, 097009 (2008)] a disorder sensitive relatively small value of the total electron-boson coupling constant lambda{tot}=lambda{e-ph}+lambda{e-sp} approximately 0.6+/-0.35 can be estimated adopting an effective single-band picture.

Model for the magnetic order and pairing channels in Fe pnictide superconductors

A two-orbital model for Fe-pnictide superconductors is investigated using computational techniques on two-dimensional square clusters. The hopping amplitudes are derived from orbital overlap integrals, or by band structure fits, and the spin frustrating effect of the plaquette-diagonal Fe-Fe hopping is remarked. A spin striped state is stable in a broad range of couplings in the undoped regime, in agreement with neutron scattering. Adding two electrons to the undoped ground state of a small cluster, the dominant pairing operators are found. Depending on the parameters, two pairing operators were identified: they involve inter-xz-yz orbital combinations forming spin singlets or triplets, transforming according to the B2g and A2g representations of the D4h group, respectively.

Pairing symmetry in a two-orbital exchange coupling model of oxypnictides

We study the pairing symmetry of a two-orbital J1-J2 model for FeAs layers in oxypnictides. We show that the mixture of an intraorbital unconventional s_{x;{2}y;{2}} approximately cos(k_{x})cos(k_{y}) pairing symmetry, which changes sign between the electron and hole Fermi surfaces, and a very small d_{x;{2}-y;{2}} approximately cos(k_{x})-cos(k_{y}) component is favored in a large part of the J1-J2 phase diagram. A pure s_{x;{2}y;{2}} pairing state is favored for J2>J1. The signs of the d_{x;{2}-y;{2}} order parameters in the two different orbitals are opposite. While a small d_{xy} approximately sin(k_{x})sin(k_{y}) interorbital pairing coexists in the above phases, the intraorbital d_{xy} pairing is not favored even for large J2.

Momentum dependence of the superconducting gap in NdFeAsO0.9F0.1 single crystals measured by angle resolved photoemission spectroscopy

We use angle resolved photoemission spectroscopy to study the momentum dependence of the superconducting gap in NdFeAsO0.9F0.1 single crystals. We find that the Gamma hole pocket is fully gapped below the superconducting transition temperature. The value of the superconducting gap is 15+/-1.5 meV and its anisotropy around the hole pocket is smaller than 20% of this value-consistent with an isotropic or anisotropic s-wave symmetry of the order parameter. This is a significant departure from the situation in the cuprates, pointing to the possibility that the superconductivity in the iron arsenic based system arises from a different mechanism.

Field and temperature dependence of the superfluid density in LaFeAsO1-xFx superconductors: a muon spin relaxation study

We present zero field and transverse field muon spin relaxation experiments on the recently discovered Fe-based superconductor LaFeAsO1-xFx (x=0.075 and x=0.1). The temperature dependence of the deduced superfluid density is consistent with a BCS s-wave or a dirty d-wave gap function, while the field dependence strongly evidences unconventional superconductivity. We obtain the in-plane penetration depth of lambda ab(0)=254(2) nm for x=0.1 and lambda ab(0)=364(8) nm for x=0.075. Further evidence for unconventional superconductivity is provided by the ratio of Tc versus the superfluid density, which is close to the Uemura line of high-Tc cuprates.