We consider the minimal two-band model for the Fe-based superconductors with a phenomenological pairing interaction which mimics short-range antiferromagnetic (AFM) fluctuations. Two superconducting (SC) gap solutions are found to exist with the model: sign-changing s-wave gap ($\pm$s-wave) and double d-wave gap states. Both solutions hold the approximate relation $Δ_{h} ^{max} N_h \approx Δ_{e} ^{max} N_e$, a generic feature of two band model with a dominant interband pairing interaction. We carried out the calculations of the SC properties of the both SC states such as the density of states, temperature dependencies of spin-lattice relaxation rate $1/T_1$, Knight shift, and penetration depth, particularly taking into account of the interband coherence factors. The results are discussed in comparison with the currently available experimental data.
It is developed a microscopic description of superconductivity in ferromagnetic materials with triplet pairing triggered by the exchange of magnetic fluctuations. Instead widely used paramagnon model we work with phenomenological spectrum of fluctuations in the orthorhombic ferromagnet with strong magnetic anisotropy. Depending of the field orientation parallel or perpendicular to the direction of spontaneous magnetization the effective amplitude of pairing interaction proves to be decreasing or increasing function of magnetic field that allows to explain the drastic difference in magnitudes o…
Recent experiments on Bi-based cuprate superconductors have revealed an unexpected enhancement of the pairing correlations near the interstitial oxygen dopant ions. Here we propose a possible mechanism -- based on local screening effects -- by which the oxygen dopants do modify the electronic parameters within the CuO_2 planes and strongly increase the superexchange coupling J. This enhances the spin pairing effects locally and may explain the observed spatial variations of the density of states and the pairing gap.
I review recent works on the symmetry and the structure of the superconducting gap in Fe-based superconductors and on the underlying pairing mechanism in these systems. The experimental data on superconductivity show very rich behavior, with potentially different symmetry of a superconducting state for different compositions of the same material. The variety of different pairing states raised the issue whether the physics of Fe-based superconductors is model-dependent or is universal, governed by a single underlying pairing mechanism. I argue that the physics is universal and that all pairing …
Josephson junctions between a $FeAs$-based superconductor with antiphase s-wave pairing and a conventional s-wave superconductor are studied. The translational invariance in a planar junction between a single crystal pnictide and an aluminum metal greatly enhances the relative weight of electron pockets in the pnictide to the critical current. In a wide doping region of the pnictide, a planar and a point contact junctions have opposite phases, which can be used to design a tri-junction ring with $π$ phase to probe the antiphase pairing.
The spin-fluctuation mechanism of superconductivity usually results in the presence of gapless or nodal quasiparticle states in the excitation spectrum. Nodal quasiparticle states are well established in copper-oxide, and heavy-fermion superconductors, but not in iron-based superconductors. Here, we study the pairing symmetry and mechanism of a new class of plutonium-based high-Tc superconductors and predict the presence of a nodal $s^{+-}$ wave pairing symmetry in this family. Starting from a density-functional theory (DFT) based electronic structure calculation we predict several three-dimen…
The multipocket Fermi surfaces of iron-based superconductors promote pairing states with both s_{+-}-wave and d_{x^2-y^2}-wave symmetry. We argue that the competition between these two order parameters could lead to a time-reversal-symmetry breaking state with s+id-pairing symmetry in the iron-based superconductors, and propose serveral scenarios in which this phase may be found. To understand the emergence of such a pairing state on a more rigorous footing, we start from a microscopic 5-orbital description representative for the pnictides. Using a combined approach of functional renormalizati…
Using functional renormalization group (FRG) approach, we analyze the $η$ pairing in a five d-orbital model for iron-pncitides. We find that the $η$ pairing between two hole pockets is a leading instability at low energy when the two hole pockets are close to a nesting condition. The result suggests that the system can spontaneously enter into a superconducting state with both normal pairing and $η$ paring and the $η$ pairing is driven by the inter-orbital antiferromagnetic exchange coupling while the normal pairing is driven by the intra-orbital antiferromagnetic ones. An effective model at l…
We present a self-consistent real space formulation of spin-fluctuation mediated d-wave pairing. By calculating all relevant inhomogeneous spin and charge susceptibilities in real space within the random phase approximation (RPA), we obtain the effective pairing interaction and study its spatial dependence near both local potential and hopping impurities. A remarkably large enhancement of the pairing interaction may be obtained near the impurity site. We discuss the relevance of our result to inhomogeneities observed by scanning tunneling spectroscopy on the surface of cuprate superconductors.
We perform a systematic quantum Monte Carlo study of the pairing correlation in the $S_4$ symmetric microscopic model for iron-based superconductors. It is found that the pairing with an extensive s-wave symmetry robustly dominates over other pairings at low temperature in reasonable parameter region. The pairing susceptibility, the effective pairing interaction and the $(π,0)$antiferromagnetic correlation strongly increase as the on-site Coulomb interaction increases, indicating the importance of the effect of electron-electron correlation. Our non-biased numerical results provide a unified u…
We discuss the influence on spin-fluctuation pairing theory of orbital selective strong correlation effects in Fe-based superconductors, particularly Fe chalcogenide systems. We propose that a key ingredient for an improved itinerant pairing theory is orbital selectivity, i.e., incorporating the reduced coherence of quasiparticles occupying specific orbital states. This modifies the usual spin-fluctuation via suppression of pair scattering processes involving those less coherent states and results in orbital selective Cooper pairing of electrons in the remaining states. We show that this parad…
We argue that the recent Raman spectroscopy observation of a sharp mode in s-wave superconducting V$_3$Si is due to a competing d-wave pairing state. We present microscopic arguments for the origin of this d-wave order. We further argue that the d-wave order explains the observed shrinking of the vortex core structure at anomalously low magnetic fields and the large anisotropy observed in the upper critical field.
We present the ground state pairing correlations in the $S_4$ symmetric microscopic model for iron-based superconductors, computed with the constrained-path Monte Carlo method. For various electron fillings and interaction strengths, we find that the $s_{xy}$ pairing dominates over other pairing correlations and is positive when the pair separation exceeds several lattice constants, whatever for iron pnictides and iron chlcogenides. These ground state properties, especially the long range part pairing correlations re-confirm the previous finite temperature results published in Phys. Rev. Lett.…
We review briefly several approaches used to investigate the stability of stripe phases in high temperature superconductors, where charge inhomogeneities arise from competing kinetic and magnetic energies. The mechanism of stripe formation, their consequences for the normal state and enhancement of pairing interaction triggered by charge inhomogeneities are briefly summarized. Finally, we demonstrate that orbital degeneracy ($i$) leads to a more subtle mechanism of stripe formation, and ($ii$) plays an important role and determines the symmetry of the superconducting state in pnictides.
In iron selenide superconductors only electron-like Fermi pockets survive, challenging the $S^{\pm}$ pairing based on the quasi-nesting between the electron and hole Fermi pockets (as in iron arsenides). By functional renormalization group study we show that an in-phase $S$-wave pairing on the electron pockets ($S^{++}_{ee}$) is realized. The pairing mechanism involves two competing driving forces: The strong C-type spin fluctuations cause attractive pair scattering between and within electron pockets via Cooperon excitations on the virtual hole pockets, while the G-type spin fluctuations caus…
We report a scaling relation between $ρ_s(0)$ and the product of the pseudogap temperature $T^{*}$, $σ_{\rm DC}$ and $T_c$, with $T^{*}$ rescaled by the maximum transition temperature $T_c^{\max}$, which holds universally in the entire doping range for the hole-doped cuprates.
We derive the effective action for superconducting fluctuations in a four-band model for pnictides, discussing the emergence of a single critical mode out of a dominant interband pairing mechanism. We then apply our model to calculate the paraconductivity in two-dimensional and layered three-dimensional systems, and compare our results with recent resistivity measurements in SmFeAsOF
Scanning tunneling microscopy (STM) has made tremendous progress in the study and understanding of both classical and unconventional superconductors. This has motivated a rapidly growing effort to apply the same techniques to the iron-based high-Tc superconductors since their discovery in 2008. Five years have brought exciting advances in imaging and spectroscopic investigation of this new class of materials. In this review, we focus on several recent STM contributions to the identification of the gap symmetry and pairing glue. We highlight the unique capabilities and challenges still ahead fo…
Its direct momentum sensitivity confers to angle-resolved photoemission spectroscopy (ARPES) a unique perspective in investigating the superconducting gap of multi-band systems. In this review we discuss ARPES studies on the superconducting gap of the high-temperature Fe-based superconductors. We show that while Fermi-surface-driven pairing mechanisms fail to provide a universal scheme for the Fe-based superconductors, theoretical approaches based on short-range interactions lead to a more robust and universal description of superconductivity in these materials. Our findings are also discussed…
The real-space localized hole pair is constructed in the Cu-O plane of the hole-doped cuprate superconductors. We prove analytically and numerically that two electrons, due to the nearest-neighbor Coulomb repulsive confinement effect, can be in pairing inside a single plaquette with the d-wave symmetry. The scenario supports the `no glue' pairing picture for the cuprates. Based on the scenarios, the physical origin of the Fermi pocket (or Fermi arc) and the two pseudogap behavior are provided. Our framework leads directly to a unified linear relationship between the pseudogap temperature T* an…
We introduce a generalized joint density of states (GJDOS), which incorporates the coherent factor into the JDOS, to study quasiparticle interference (QPI) in superconductors. The intimate relation between the Fourier-transformed local density of states and GJDOS is revealed: they corre- spond respectively to the real and imaginary parts of a generalized impurity-response function, and particularly share the same angular factors and singular boundaries, as seen from our approximate analytic results for d-wave superconductors. Remarkably, our numerical GJDOS analysis agrees well with the QPI pa…
We show that the newly discovered BiS$_2$-based superconductors may have a dominant triplet pairing component, in addition to a subdominant singlet component arising from the spin-orbital coupling. The pairing respects time-reversal symmetry. The dominant triplet gap causes gap sign changes between the spin-split Fermi pockets. Within a pocket, the gap function respects $d^*_{x^2-y^2}$-wave symmetry, where the star indicates joint spin-lattice rotations. Below the Lifshitz filling level the gap is nodelss and the superconducting state is weak topological. Above the Lifshitz points the gap beco…
We have studied the effect of a single nonmagnetic impurity in the recently discovered (K,Tl)Fe$_x$Se$_2$ superconductors, within both a toy two-band model and a more realistic five-band model. We have found that, out of five types of pairing symmetry under consideration, only the $d_{x^2-y^2}$-wave pairing gives rise to impurity resonance states. The intra-gap states have energies far away from the Fermi energy. The existence of these intra-gap states is robust against the presence or absence of inter-band scattering. However, the inter-band scattering does tune the relative distribution of l…
We analyze a simple model containing the physical ingredients of a Hund's metal, the local spin fluctuations with power-law correlators, $(Ω_0/|Ω|)^γ$, with $γ$ greater than one, interacting with electronic quasiparticles. While the critical temperature and the gap change significantly with varying parameters, the $2Δ_{max}/k_BT_c$ remains close to twice the BCS value in agreement with experimental observations in the iron-based superconductors (FeSC).
We study s-wave Cooper pairing in heavy-fermion systems. We analyze the periodic Anderson model by means of the variational cluster approach (VCA) focusing on the interorbital Cooper pairing between a conduction electron ($c$ electron) and an $f$ electron, called the "$c$-$f$ pairing." It is shown that the s-wave superconductivity appears coexisting with long-range antiferromagnetic order when electrons or holes are doped into the system at half filling. The antiferromagnetic order vanishes when the doping concentration exceeds a certain critical value, leading to a pure s-wave superconducting…
We report the finding of a novel pairing state in a newly discovered superconductor Na$_2$Cr$_3$As$_3$. This material has a noncentrosymmetric quasi-one-dimensional crystal structure and is superconducting at $T_{\mathrm{C}}\sim$ 8.0 K. We find that the magnetic penetration depth data suggests the presence of a nodal line $p_z$-wave pairing state with zero magnetic moment using transverse-field muon-spin rotation (TF-$μ$SR) measurements. The nodal gap observed in Na$_2$Cr$_3$As$_3$ compound is consistent with that observed in isostructural (K,Cs)$_2$Cr$_3$As$_3$ compounds using TF-$μ$SR measur…
Triplet pairing, orbital selectivity and correlations in Iron-based superconductors
University of Cincinnati（辛辛那提大学）；Max-Planck-Institut für Festkörperforschung（马克斯·普朗克固体研究所）；Rutgers University（罗格斯大学）；Royal Holloway, University of London（伦敦大学皇家霍洛威学院）
The origin of the exceptionally strong superconductivity of cuprates remains a subject of debate after more than two decades of investigation. Here we follow a new lead: The onset temperature for superconductivity scales with the strength of the anomalous normal-state scattering that makes the resistivity linear in temperature. The same correlation between linear resistivity and Tc is found in organic superconductors, for which pairing is known to come from fluctuations of a nearby antiferromagnetic phase, and in pnictide superconductors, for which an antiferromagnetic scenario is also likely.…
We study the dynamics of the Cooper pairing across the T=0 phase diagram of the two-dimensional Hubbard Model, relevant for high-temperature superconductors, using a cluster extension of dynamical mean field theory. We find that the superconducting pairing function evolves from an unconventional form in the over-doped region into a more conventional boson-mediated retarded form in the under-doped region of the phase diagram. The boson, however, promotes the rise of a pseudo-gap in the electron density of states rather than a superconducting gap as in the standard theory of superconductivity. W…
Conventional Cooper pairing arises from attractive interaction of electrons in the metallic bands. Recent experiment on Co-doped LiFeAs shows superconductivity in the insulating valence band, which is evolved from a metallic hole band upon doping. Here we examine this phenomenon by studying superconductivity in a three-orbital Hamiltonian relevant to the doped LiFeAs. We show explicitly that Cooper pairing of the insulating hole band requires a finite pairing interaction strength. For strong coupling, the superconductivity in the hole band is robust against the sink of the hole band below the …
Muon spin rotation and relaxation experiments on the centrosymmetric intermetallic superconductor LaNiGa$_2$ are reported. The appearance of spontaneous magnetic fields coincides with the onset of superconductivity, implying that the superconducting state breaks time reversal symmetry, similarly to non-centrosymmetric LaNiC$_2$. Only four triplet states are compatible with this observation, all of which are non-unitary triplets. This suggests that LaNiGa$_2$ is the centrosymmetric analogue of LaNiC$_2$. We argue that these materials are representatives of a new family of paramagnetic non-unita…
The nature of the pairing state in iron-based superconductors is the subject of much debate. Here we argue that in one material, the stoichiometric iron pnictide KFe2As2, there is overwhelming evidence for a d-wave pairing state, characterized by symmetry-imposed vertical line nodes in the superconducting gap. This evidence is reviewed, with a focus on thermal conductivity and the strong impact of impurity scattering on the critical temperature Tc. We then compare KFe2As2 to Ba0.6K0.4Fe2As2, obtained by Ba substitution, where the pairing symmetry is s-wave and the Tc is ten times higher. The t…
The origin of the high temperature superconductivity in the iron-based superconductors remains elusive after being extensively studied for more than a decade. Determination of the pairing symmetry is essential in understanding the superconductivity mechanism. In the iron-based superconductors that have hole pockets around the Brillouin zone center and electron pockets around the zone corners, the pairing symmetry is generally considered to be s$_\pm$, endowing a sign change in the superconducting gap between the hole and electron pockets. For the iron-based superconductors with only hole pocke…
In a recent Letter [PRL 103, 186402 (2009)], the energy band structure of Fe-As-based superconductors is fitted with a tight-binding model with two Fe ions per unit cell and two degenerate xz and yz orbitals per Fe ion. The author claims that the proposed model, which differs markedly from a model previously used by other authors for the same two orbitals in the same compounds, possesses the symmetry required to describe the Fe-As planes in iron-pnictide superconductors. In this comment we argue that this is not the case.
The electronic states of the FeAs plane in iron-based superconductors are investigated on the basis of the two-dimensional 16-band d-p model, where the tight-binding parameters are determined so as to fit the band structure obtained by the density functional calculation for LaFeAsO. The model includes the Coulomb interaction on a Fe site: the intra- and inter-orbital direct terms U and U', the exchange coupling J and the pair-transfer J'. Within the random phase approximation (RPA), we discuss the pairing symmetry of possible superconducting states including s-wave and d-wave pairing on the U'…
We give an extensive treatment of the pairing symmetry in the ferromagnetic superconductor $UGe_{2}$. We show that one can draw important conclusions concerning the superconducting state, considering only the transformation properties of the pairing function, without assumptions about the form of the pairing amplitudes.
We investigate how hybridization (single-quasiparticle scattering) between two superconducting bands induces odd-frequency superconductivity in a multiband superconductor. An explicit derivation of the odd-frequency pairing correlation and its full frequency dependence is given. We find that the density of states is modified, from the sum of the two BCS spectra, at higher energies by additional hybridization gaps with strong coherence peaks when odd-frequency pairing is present.
