D-wave Pairing Research Articles

Competing superconducting channels in iron pnictides from the strong coupling theory with biquadratic spin interactions

We study the symmetry and strength of the superconducting pairing in a two-orbital model for iron pnictides using the slave boson strong coupling approach. We show that the nearest-neighbor biquadratic interaction strongly affects the superconducting pairing phase diagram by promoting the B1g and the A1g channels. The resulting phase diagram consists of several competing pairing channels, including the isotropic A1g channel, an anisotropic B1g channel, and two pairing channels. We have investigated the evolution of superconducting states with electron doping, and find that the biquadratic interaction plays a crucial role in stabilizing the and even pure d-wave pairing in the heavily electron- and hole-doped regimes. In addition, we identify a novel orbital-B1g pairing channel, which has a s-wave form factor but a B1g symmetry. This channel has a comparable pairing amplitude to the d-wave pairing, and may strongly influence the superconducting gap anisotropy of the system in the overdoped regime. These findings are crucial in understanding the doping evolution of the superconducting gap anisotropy observed by angle resolved photoemission spectroscopy in the iron pnictides and iron chalcogenides, including the heavily K-doped BaFe2As2 and K-doped FeSe films.

Detecting a preformed pair phase: Response to a pairing forcing field

The normal state of strongly coupled superconductors is characterized by the presence of "preformed" Cooper pairs well above the superconducting critical temperature. In this regime, the electrons are paired, but they lack the phase coherence necessary for superconductivity. The existence of preformed pairs implies the existence of a characteristic energy scale associated to a pseudogap. Preformed pairs are often invoked to interpret systems where some signatures of pairing are present without actual superconductivity, but an unambiguous theoretical characterization of a preformed-pair system is still lacking. To fill this gap, we consider the response to an external pairing field of an attractive Hubbard model, which hosts one of the cleanest realizations of a preformed pair phase, and a repulsive model where s-wave superconductivity can not be realized. Using dynamical mean-field theory to study this response, we identify the characteristic features which distinguish the reaction of a preformed pair state from a normal metal without any precursor of pairing. The theoretical detection of preformed pairs is associated with the behavior of the second derivative of the order parameter with respect to the external field, as confirmed by analytic calculations in limiting cases. Our findings provide a solid testbed for the interpretation of state-of-the-art calculations for the normal state of the doped Hubbard model in terms of d-wave preformed pairs and, in perspective, of non-equilibrium experiments in high-temperature superconductors.

Topological Septet Pairing with Spin-32Fermions: High-Partial-Wave Channel Counterpart of theHe3−BPhase

We systematically generalize the exotic ^{3}He-B phase, which not only exhibits unconventional symmetry but is also isotropic and topologically nontrivial, to arbitrary partial-wave channels with multicomponent fermions. The concrete example with four-component fermions is illustrated including the isotropic f-, p-, and d-wave pairings in the spin septet, triplet, and quintet channels, respectively. The odd partial-wave channel pairings are topologically nontrivial, while pairings in even partial-wave channels are topologically trivial. The topological index reaches the largest value of N^{2} in the p-wave channel (N is half of the fermion component number). The surface spectra exhibit multiple linear and even high order Dirac cones. Applications to multiorbital condensed matter systems and multicomponent ultracold large spin fermion systems are discussed.

Enhancement of the d-wave pairing correlations by charge and spin ordering in the spin-one-half Falicov-Kimball model with Hund and Hubbard coupling

The projector quantum Monte Carlo method is used to examine the effects of the spin-independent Ufd as well as spin-dependent Jz Coulomb interaction between the localized f and itinerant d electrons on the stability of various types of charge/spin ordering and superconducting correlations in the spin-one-half Falicov-Kimball model with Hund and Hubbard coupling. The model is studied for a wide range of f- and d-electron concentrations and it is found that the interband interactions Ufd and Jz stabilize three basic types of charge/spin ordering, namely, i) the axial striped phases, ii) the regular n-molecular phases and iii) the phase-separated states. It is shown that the d-wave pairing correlations are enhanced within the axial striped and phase-separated states, but not in the regular phases. Moreover, it was found that the antiferromagnetic spin arrangement within the chains further enhances the d-wave paring correlations, while the ferromagnetic one has a fully opposite effect.

Anisotropic Upper Critical Field of Iron-Based Superconductors

The upper critical field and its anisotropy are the easiest properties to examine in the research of iron-based superconductors. Based on warped cylindrical Fermi surface models, we investigate the temperature and angle dependence of the upper critical field in detail by employing the quasi-classical formalism of the Werthamer–Helfand–Hohenberg (WHH) theory. Our numerical results reveal the anisotropy of the upper critical field, which may be caused by an anisotropic gap function (e.g., d-wave pairing) or an anisotropic Fermi surface, respectively. Further, according to our analysis, this anisotropy can be modulated by the deformation of the Fermi surface and will be strongly suppressed by the Pauli paramagnetic effect.

Structural analysis of the precursor pseudogap in cuprate superconductors

Abstract We investigate the precursor pseudogap (PP) state that emerges on the lower temperature side of the pseudogap phase in cuprate superconductors based on the characteristic layer structure. The coherence among layers in the electronic state may be broken by low energy thermal interactions, whereas the coherence within the layers remains in the phase above the superconducting (SC) phase on account of strongness of the bonding. In this state, the two-electron energy gain (TEG) is also larger than that of SC state and the one-electron energy gain (OEG) is smaller than that of the SC state. We call this incoherent ensemble of in-layer states the in-layer electronic state system (IESS). The PP state is a crossover state between IESS and the normal pseudogap (NP) state, which appears on the upper temperature side, because the d-wave pairing symmetry in cuprates inverts the sign of the difference of the total electronic energy gain between the IESS and the NP state around the nodal region, even though it is positive overall. We perform our analysis at the mean field level. We show that the relationships among the SC gap, the gap of in-layer state, and the transition temperatures in the relevant phases are compatible with existing experimental data. The proposed precursor state requires pairing models to make the SC interactions three-dimensional beyond a single layer, although the precursors have in-layer properties.

Speed of Sound of a Spin-Balanced Fermi Gas with s- and d-Wave Pairings Across the BCS–BEC Evolution

The authors of a recent paper (PRA \textbf{87}, 013613 (2013)) argued that in fermionic systems with d-wave pairing the speed of sound is nonanalytic across the BCS-BEC crossover at the point where the chemical potential vanishes, regardless of the specific details of the interaction potential. On the contrary, the numerical results reported here suggest that the speed of sound across the BCS-BEC evolution of atomic Fermi gases with s- and d-wave pairings in two-dimensional square lattices is a smooth analytic function at the vanishing chemical potential.

Thermodynamics of the d-wave pairing in organic superconductors

Organic superconductors with [Formula: see text]-type structure are most frequently identified as nodal gap superconductors from the experimental observation of a power-law behavior in the low-temperature thermodynamic properties such as specific heat capacity. We perform series of theoretical calculations of specific heat capacity of three typical organic complexes with different transition temperatures by using Bogolyubov–de Gennes equations. The good agreement between the experimental data and the calculations demonstrates that the [Formula: see text]-wave pairing is certainly realized in these superconductors.

Concealed d-wave pairs in the s± condensate of iron-based superconductors

A central question in iron-based superconductivity is the mechanism by which the paired electrons minimize their strong mutual Coulomb repulsion. In most unconventional superconductors, Coulomb repulsion is minimized through the formation of higher angular momentum Cooper pairs, with Fermi surface nodes in the pair wavefunction. The apparent absence of such nodes in the iron-based superconductors has led to a belief they form an s-wave ([Formula: see text]) singlet state, which changes sign between the electron and hole pockets. However, the multiorbital nature of these systems opens an alternative possibility. Here, we propose a new class of [Formula: see text] state containing a condensate of d-wave Cooper pairs, concealed by their entanglement with the iron orbitals. By combining the d-wave ([Formula: see text]) motion of the pairs with the internal angular momenta [Formula: see text] of the iron orbitals to make a singlet ([Formula: see text]), an [Formula: see text] superconductor with a nontrivial topology is formed. This scenario allows us to understand the development of octet nodes in potassium-doped Ba1-x KXFe2As2 as a reconfiguration of the orbital and internal angular momentum into a high spin ([Formula: see text]) state; the reverse transition under pressure into a fully gapped state can then be interpreted as a return to the low-spin singlet. The formation of orbitally entangled pairs is predicted to give rise to a shift in the orbital content at the Fermi surface, which can be tested via laser-based angle-resolved photoemission spectroscopy.

Thermodynamic Evidence of d-Wave Superconductivity of the Organic Superconductor λ-(BETS)2GaCl4

Low-temperature heat capacity of the organic superconductor λ-(BETS)2GaCl4 in a temperature range between 0.6 and 10 K was measured for a single crystal sample by relaxation calorimetry technique. The contribution of electronic heat capacity in the superconducting state shows T2 dependence at lower temperature that indicates the existence of quasi-particle excitations from the line-nodal gap structure of d-wave pairing. The recovery of the electronic heat capacity coefficient, γ by magnetic field shows H1/2 dependence that is consistent with the picture of line-nodal superconductor. In spite of the different packing from typical organic superconductors κ-(BEDT-TTF)2X, the λ-type BETS salt also shows a feature of d-wave symmetry pairing.

Time-Reversal Invariant Topological Superconductivity in Quasi-One-Dimensional Structures

It is shown that a time-reversal invariant topological superconductivity can be realized in a quasi-onedimensional structure, which is fabricated by filling the superconducting materials into the periodic channel of dielectric matrices like zeolite and asbestos under high pressure. The topological superconducting phase sets up in the presence of large spin-orbit interactions when s-wave intra-wire and d-wave inter-wire pairings take place. Kramers pairs of Majorana bound states emerge at the edges of each wire. The time-reversal topological superconductor belongs to DIII class of symmetry with a Z2 invariant.

Pairing mechanism of the high temperature superconductors

The pairing mechanism of the high temperature superconductors is one of the most important issues in the study of the high temperature superconductivity. After the intensive investigation in the past three decades, it is now commonly accepted that the d-wave pairing in the high temperature superconductors is driven by the exchange of the antiferromagnetic spin fluctuation in the system. However, an open problem remains: how to understand the complex phase diagram of the high temperature superconductors, especially the anomalous behaviors related to the pseudogap phenomena in the under- doped regime. The key to the answer of this question lies in the local-itinerant dualism of the electron in these systems.

Theory of High-Temperature Superconductivity in Cuprates

We propose a microscopic theory of superconductivity for systems with strong electron correlations such as cuprates in the framework of the extended Hubbard model where the intersite Coulomb repulsion and electron-phonon interaction (EPI) are taken into account. The Dyson equation for the normal and pair Green functions for the Hubbard operators (HOs) is derived. Due to the unconventional commutation relations for the HOs, a specific kinematical interaction of electrons with spin and charge fluctuations with a large coupling constant of the order of the kinetic energy of electrons W emerges that results in the d-wave pairing with high- Tc. Superconductivity can be suppressed only for a large intersite Coulomb repulsion \(V \gtrsim W\). Isotope effect on Tc caused by electron-phonon interaction is weak at optimal doping and increases at low doping. The kinematical interaction is absent in the spin-fermion models and is lost in the slave-boson (-fermion) models treated in the mean-field approximation.

Topological superconductivity and the fractional Josephson effect in quasi-one dimensional wires on a plane

A time-reversal invariant topological superconductivity is suggested to be realized in a quasi-one dimensional structure on a plane, which is fabricated by filling the superconducting materials into the periodic channel of dielectric matrices like zeolite and asbestos under high pressure. The topological superconducting phase sets up in the presence of large spin-orbit interactions when intra-wire s-wave and inter-wire d-wave pairings take place. Kramers pairs of Majorana bound states emerge at the edges of each wire. We analyze effects of Zeeman magnetic field on Majorana zero-energy states. In-plane magnetic field was shown to make asymmetric the energy dispersion, nevertheless Majorana fermions survive due to protection of a particle-hole symmetry. Tunneling of Majorana quasi-particle from the end of one wire to the nearest-neighboring one yields edge fractional Josephson current with $4\pi$-periodicity.

Consistent picture of the octet-nodal gap and its evolution with doping in heavily overdoped Ba1−xKxFe2As2

We investigate the pairing symmetry in heavily overdoped Ba1−xKxFe2As2 based on the spin-fluctuation mechanism. We propose a Fermi-patch mechanism that is different from the conventional Fermi-surface-nesting picture. The exotic octet nodes of the superconducting gap and the unusual evolution of the gap with doping observed by the recent experiments are well explained in a unified manner. We demonstrate that the scattering of electrons on the Fermi patches is mainly responsible for the incommensurate spin fluctuations and consequently the Fermi-surface-dependent multi-gap structure, since the Fermi level is close to the flat band. In addition, we find that a d-wave pairing state will prevail over the s-wave pairing state around the Lifshitz transition point.

Intrinsic thermal Hall conductivity in the mixed state ofd-wave superconductors: From wave-packet dynamics to scaling

Recent numerical calculation of the intrinsic thermal Hall conductivity of nodal d-wave superconductors in the mixed state revealed a rapid increase of this quantity above an onset temperature. Interestingly, this defines a measurable energy scale in an otherwise gapless state. Using the mathematics of magnetic coherent states, in this paper such energy scale is related to a dynamical process associated with the Andreev scattering of an electron wavepacket moving along the constant energy contours in the momentum space. This energy scale is then used to obtain an improved scaling collapse of numerically calculated thermal Hall conductivity in a tight-binding model as a function of temperature, magnetic field and the d-wave pairing amplitude at various band fillings. The results indicate that the mentioned onset temperature is associated with the ability of the quasiparticle wavepacket to complete its semiclassical orbit before it is appreciably scattered by the superconducting condensate.

Intertwined orders from symmetry projected wavefunctions of repulsively interacting Fermi gases in optical lattices

Unconventional strongly correlated phases of the repulsive Fermi–Hubbard model, which could be emulated by ultracold vapors loaded in optical lattices, are investigated by means of energy minimizations with quantum number projection before variation and without any assumed order parameter. Using a tube-like geometry of optical plaquettes to realize the four-leg ladder Hubbard Hamiltonian, we highlight the intertwining of spin-, charge-, and pair-density waves embedded in a uniform d-wave superfluid background. As the lattice filling increases, this phase emerges from homogenous states exhibiting spiral magnetism and evolves towards a doped antiferromagnet. A concomitant enhancement of long-ranged d-wave pairing correlations is also found. Numerical tests of the approach for two-dimensional clusters are carried out, too.

Observation of two-dimensional bulk electronic states in the superconducting topological insulator heterostructureCux(PbSe)5(Bi2Se3)6: Implications for unconventional superconductivity

We have performed angle-resolved photoemission spectroscopy (ARPES) on Cux(PbSe)5(Bi2Se3)6 (CPSBS; x = 1.47), a superconductor derived from a topological insulator heterostructure, to elucidate the electronic states relevant to the occurrence of possible unconventional superconductivity. Upon Cu intercalation into the parent compound (PbSe)5(Bi2Se3)6, we observed a distinct energy shift of the bulk conduction band due to electron doping. Photon-energy dependent ARPES measurements of CPSBS revealed that the observed bulk band forms a cylindrical electronlike Fermi surface at the Brillouin-zone center. The two-dimensional nature of the bulk electronic states suggests the occurrence of odd-parity Eu pairing or even-parity d-wave pairing, both of which may provide a platform of Majorana bound states in the superconducting state.

In-Plane Anisotropy of Upper Critical Field and Flux-Flow Resistivity in Layered Organic Superconductor β′′-(ET)2SF5CH2CF2SO3

We report the in-plane anisotropy of the upper critical field (Hc2) and the flux-flow resistivity (FFR) for a layered organic superconductor β′′-(ET)2SF5CH2CF2SO3 with the incoherent nature of the interlayer transport. The in-plane angular dependence of Hc2 showed a fourfold oscillation with maxima in the directions around H || b and a axes. This result is compatible with a \(d_{x^{2} - y^{2}}\) order parameter. The determined nodal structure is consistent with theoretical predictions of superconductivity mediated by charge fluctuations. Moreover, the dependence of the FFR on in-plane field-orientation showed a fourfold symmetry with cusp-like minima in the directions around H || b and a axes, which is very similar to the FFR for κ-(ET)2Cu(NCS)2 with d-wave pairing symmetry. From these results, we claim that the vortex dynamics is strongly affected by the superconducting gap structure for highly two-dimensional superconductors with d-wave pairing symmetry.

Controlled pairing symmetry of the superfluid state in systems of three-component repulsive fermionic atoms in optical lattices

We investigate the pairing symmetry of the superfluid state in repulsively interacting three-component (colors) fermionic atoms in optical lattices. When two of the three color-dependent repulsions are much larger than the other, pairing symmetry is an extended s wave, although the superfluid state appears adjacent to the paired Mott insulator in the phase diagram. As the difference between the three repulsions is decreased in square optical lattices, the extended s-wave pairing changes into a nodal s-wave pairing and then into a d-wave pairing. This change in pairing symmetry is attributed to the competition among the density fluctuations of unpaired atoms, the quantum fluctuations of the color-density wave, and those of the color-selective antiferromagnet. This phenomenon can be studied using existing experimental techniques.We investigate the pairing symmetry of the superfluid state in repulsively interacting three-component (color) fermionic atoms in optical lattices. When two of the three color-dependent repulsions are much stronger than the other, pairing symmetry is an extended $s$ wave although the superfluid state appears adjacent to the paired Mott insulator in the phase diagram. On the other hand, when two of the three color-dependent repulsions are weaker than the other, pairing symmetry is a d_{x^2-y^2}-wave. This change in pairing symmetry is attributed to the change in the dominant quantum fluctuations from the density fluctuations of unpaired atoms and the color-density wave fluctuations to the color-selective antiferromagnet fluctuations. This phenomenon can be studied using existing experimental techniques.