Iron pnictides and chalcogenides: a new paradigm for superconductivity.

Superconductivity is a remarkably widespread phenomenon that is observed in most metals cooled to very low temperatures. The ubiquity of such conventional superconductors, and the wide range of associated critical temperatures, is readily understood in terms of the well-known Bardeen-Cooper-Schrieffer theory. Occasionally, however, unconventional superconductors are found, such as the iron-based materials, which extend and defy this understanding in unexpected ways. In the case of the iron-based superconductors, this includes the different ways in which the presence of multiple atomic orbitals can manifest in unconventional superconductivity, giving rise to a rich landscape of gap structures that share the same dominant pairing mechanism. In addition, these materials have also led to insights into the unusual metallic state governed by the Hund's interaction, the control and mechanisms of electronic nematicity, the impact of magnetic fluctuations and quantum criticality, and the importance of topology in correlated states. Over the fourteen years since their discovery, iron-based superconductors have proven to be a testing ground for the development of novel experimental tools and theoretical approaches, both of which have extensively influenced the wider field of quantum materials.

Atomic-scale electronic structure of the cuprate pair density wave state coexisting with superconductivity.

The defining characteristic of hole-doped cuprates is d-wave high temperature superconductivity. However, intense theoretical interest is now focused on whether a pair density wave state (PDW) could coexist with cuprate superconductivity [D. F. Agterberg et al., Annu. Rev. Condens. Matter Phys. 11, 231 (2020)]. Here, we use a strong-coupling mean-field theory of cuprates, to model the atomic-scale electronic structure of an eight-unit-cell periodic, d-symmetry form factor, pair density wave (PDW) state coexisting with d-wave superconductivity (DSC). From this PDW + DSC model, the atomically resolved density of Bogoliubov quasiparticle states [Formula: see text] is predicted at the terminal BiO surface of Bi2Sr2CaCu2O8 and compared with high-precision electronic visualization experiments using spectroscopic imaging scanning tunneling microscopy (STM). The PDW + DSC model predictions include the intraunit-cell structure and periodic modulations of [Formula: see text], the modulations of the coherence peak energy [Formula: see text] and the characteristics of Bogoliubov quasiparticle interference in scattering-wavevector space [Formula: see text] Consistency between all these predictions and the corresponding experiments indicates that lightly hole-doped Bi2Sr2CaCu2O8 does contain a PDW + DSC state. Moreover, in the model the PDW + DSC state becomes unstable to a pure DSC state at a critical hole density p*, with empirically equivalent phenomena occurring in the experiments. All these results are consistent with a picture in which the cuprate translational symmetry-breaking state is a PDW, the observed charge modulations are its consequence, the antinodal pseudogap is that of the PDW state, and the cuprate critical point at p* ≈ 19% occurs due to disappearance of this PDW.

Anisotropic spin fluctuations in detwinned FeSe.

Superconductivity in FeSe emerges from a nematic phase that breaks four-fold rotational symmetry in the iron plane. This phase may arise from orbital ordering, spin fluctuations or hidden magnetic quadrupolar order. Here we use inelastic neutron scattering on a mosaic of single crystals of FeSe, detwinned by mounting on a BaFe2As2 substrate to demonstrate that spin excitations are most intense at the antiferromagnetic wave vectors QAF = (±1, 0) at low energies E = 6-11 meV in the normal state. This two-fold (C2) anisotropy is reduced at lower energies, 3-5 meV, indicating a gapped four-fold (C4) mode. In the superconducting state, however, the strong nematic anisotropy is again reflected in the spin resonance (E = 3.6 meV) at QAF with incommensurate scattering around 5-6 meV. Our results highlight the extreme electronic anisotropy of the nematic phase of FeSe and are consistent with a highly anisotropic superconducting gap driven by spin fluctuations.

Imaging orbital-selective quasiparticles in the Hund's metal state of FeSe.

Strong electronic correlations, emerging from the parent Mott insulator phase, are key to copper-based high-temperature superconductivity. By contrast, the parent phase of an iron-based high-temperature superconductor is never a correlated insulator. However, this distinction may be deceptive because Fe has five actived d orbitals while Cu has only one. In theory, such orbital multiplicity can generate a Hund's metal state, in which alignment of the Fe spins suppresses inter-orbital fluctuations, producing orbitally selective strong correlations. The spectral weights Zm of quasiparticles associated with different Fe orbitals m should then be radically different. Here we use quasiparticle scattering interference resolved by orbital content to explore these predictions in FeSe. Signatures of strong, orbitally selective differences of quasiparticle Zm appear on all detectable bands over a wide energy range. Further, the quasiparticle interference amplitudes reveal that [Formula: see text], consistent with earlier orbital-selective Cooper pairing studies. Thus, orbital-selective strong correlations dominate the parent state of iron-based high-temperature superconductivity in FeSe.

Knight Shift and Leading Superconducting Instability from Spin Fluctuations in Sr_{2}RuO_{4}.

Recent nuclear magnetic resonance studies [A. Pustogow et al., Nature 574, 72 (2019)] have challenged the prevalent chiral triplet pairing scenario proposed for Sr_{2}RuO_{4}. To provide guidance from microscopic theory as to which other pair states might be compatible with the new data, we perform a detailed theoretical study of spin fluctuation mediated pairing for this compound. We map out the phase diagram as a function of spin-orbit coupling, interaction parameters, and band structure properties over physically reasonable ranges, comparing when possible with photoemission and inelastic neutron scattering data information. We find that even-parity pseudospin singlet solutions dominate large regions of the phase diagram, but in certain regimes spin-orbit coupling favors a near-nodal odd-parity triplet superconducting state, which is either helical or chiral depending on the proximity of the γ band to the van Hove points. A surprising near degeneracy of the nodal s^{'} and d_{x^{2}-y^{2}} wave solutions leads to the possibility of a near-nodal time-reversal symmetry broken s^{'}+id_{x^{2}-y^{2}} pair state. Predictions for the temperature dependence of the Knight shift for fields in and out of plane are presented for all states.

Raising the Critical Temperature by Disorder in Unconventional Superconductors Mediated by Spin Fluctuations.

We propose a mechanism whereby disorder can enhance the transition temperature T_{c} of an unconventional superconductor with pairing driven by exchange of spin fluctuations. The theory is based on a self-consistent real space treatment of pairing in the disordered one-band Hubbard model. It has been demonstrated before that impurities can enhance pairing by softening the spin fluctuations locally; here, we consider the competing effect of pair breaking by the screened Coulomb potential also present. We show that, depending on the impurity potential strength and proximity to magnetic order, this mechanism results in a weakening of the disorder-dependent T_{c}-suppression rate expected from Abrikosov-Gor'kov theory, or even in disorder-generated T_{c} enhancements.

Probing the Pairing Interaction and Multiple Bardasis-Schrieffer Modes Using Raman Spectroscopy.

In unconventional superconductors, understanding the form of the pairing interaction is the primary goal. In this regard, Raman spectroscopy is a very useful tool, as it identifies the ground state and also the subleading pairing channels by probing collective modes. Here, we propose a general theory for a multiband Raman response and identify new features in the spectrum that can provide a robust test for a pairing theory. We identify multiple Bardasis-Schrieffer type collective modes and connect the weights of these modes to the subleading gap structures within a microscopic pairing theory. While our conclusions are completely general, we apply our approach to interpret the specific case of B_{1g} Raman scattering in hole-doped BaFe_{2}As_{2}.

High T_{c} via Spin Fluctuations from Incipient Bands: Application to Monolayers and Intercalates of FeSe.

We investigate superconductivity in a two-band system with an electronlike and a holelike band, where one of the bands is away from the Fermi level (or "incipient"). We argue that the incipient band contributes significantly to spin-fluctuation pairing in the strong coupling limit where the system is close to a magnetic instability and can lead to a large T_{c}. In this case, T_{c} is limited by a competition between the frequency range of the coupling (set by an isolated paramagnon) and the coupling strength itself, such that a domelike T_{c} dependence on the incipient band position is obtained. The coupling of electrons to phonons is found to further enhance T_{c}. The results are discussed in the context of experiments on monolayers and intercalates of FeSe.

Publisher's Note: Effects of Lifshitz Transitions on Charge Transport in Magnetic Phases of Fe-Based Superconductors [Phys. Rev. Lett. 114, 097003 (2015)].

This corrects the article DOI: 10.1103/PhysRevLett.114.097003.

Model of Electronic Structure and Superconductivity in Orbitally Ordered FeSe.

We provide a band structure with low-energy properties consistent with recent photoemission and quantum oscillation measurements on FeSe, assuming mean-field-like site- and/or bond-centered ferro-orbital ordering at the structural transition. We show how the resulting model provides a consistent explanation of the temperature dependence of the measured Knight shift and the spin-relaxation rate. Furthermore, the superconducting gap structure obtained from spin-fluctuation theory exhibits nodes on the electron pockets, consistent with the V-shaped density of states obtained by tunneling spectroscopy on this material, and the temperature dependence of the London penetration depth.

Glide-plane symmetry and superconducting gap structure of iron-based superconductors.

We consider the effect of glide-plane symmetry of the Fe-pnictogen/chalcogen layer in Fe-based superconductors on pairing in spin fluctuation models. Recent theories have proposed that so-called η-pairing states with nonzero total momentum can be realized and possess exotic properties such as odd parity spin singlet symmetry and time-reversal symmetry breaking. Here we show that η pairing is inevitable when there is orbital weight at the Fermi level from orbitals with even and odd mirror reflection symmetry in z; however, by explicit calculation, we conclude that the gap function that appears in observable quantities is identical to that found in earlier, 1 Fe per unit cell pseudocrystal momentum calculations.

Interpretation of scanning tunneling quasiparticle interference and impurity states in cuprates.

We apply a recently developed method combining first principles based Wannier functions with solutions to the Bogoliubov-de Gennes equations to the problem of interpreting STM data in cuprate superconductors. We show that the observed images of Zn on the surface of Bi_{2}Sr_{2}CaCu_{2}O_{8} can only be understood by accounting for the tails of the Cu Wannier functions, which include significant weight on apical O sites in neighboring unit cells. This calculation thus puts earlier crude "filter" theories on a microscopic foundation and solves a long-standing puzzle. We then study quasiparticle interference phenomena induced by out-of-plane weak potential scatterers, and show how patterns long observed in cuprates can be understood in terms of the interference of Wannier functions above the surface. Our results show excellent agreement with experiment and enable a better understanding of novel phenomena in the cuprates via STM imaging.

Effects of Lifshitz transition on charge transport in magnetic phases of Fe-based superconductors.

The unusual temperature dependence of the resistivity and its in-plane anisotropy observed in the Fe-based superconducting materials, particularly Ba(Fe_{1-x}Co_{x})_{2}As_{2}, has been a long-standing puzzle. Here, we consider the effect of impurity scattering on the temperature dependence of the average resistivity within a simple two-band model of a dirty spin density wave metal. The sharp drop in resistivity below the Néel temperature T_{N} in the parent compound can only be understood in terms of a Lifshitz transition following Fermi surface reconstruction upon magnetic ordering. We show that the observed resistivity anisotropy in this phase, arising from nematic defect structures, is affected by the Lifshitz transition as well.

Emergent defect states as a source of resistivity anisotropy in the nematic phase of iron pnictides.

We consider the role of potential scatterers in the nematic phase of Fe-based superconductors above the transition temperature to the (π, 0) magnetic state but below the orthorhombic structural transition. The anisotropic spin fluctuations in this region can be frozen by disorder, to create elongated magnetic droplets whose anisotropy grows as the magnetic transition is approached. Such states act as strong anisotropic defect potentials that scatter with much higher probability perpendicular to their length than parallel, although the actual crystal symmetry breaking is tiny. We calculate the scattering potentials, relaxation rates, and conductivity in this region and show that such emergent defect states are essential for the transport anisotropy observed in experiments.

Effects of disordered Ru substitution in BaFe2As2: possible realization of superdiffusion in real materials.

An unexpected insensitivity of the Fermi surface to impurity scattering is found in Ru substituted BaFe(2)As(2) from first-principles theory, offering a natural explanation of the unusual resilience of transport and superconductivity to a high level of disordered substitution in this material. This robustness is shown to originate from a coherent interference of correlated on-site and intersite impurity scattering, similar in spirit to the microscopic mechanism of superdiffusion in one dimension. Our result also demonstrates a strong substitution dependence of the Fermi surface and carrier concentration and provides a resolution to current discrepancies in recent photoelectron spectroscopy. These effects offer a natural explanation of the diminishing long-range magnetic, orbital, and superconducting orders with high substitution.

Mechanism for fluctuating pair density wave.

In weakly coupled BCS superconductors, only electrons within a tiny energy window around the Fermi energy, EF, form Cooper pairs. This may not be the case in strong coupling superconductors such as cuprates, FeSe, SrTiO3 or cold atom condensates where the pairing scale, EB, becomes comparable or even larger than EF. In cuprates, for example, a plausible candidate for the pseudogap state at low doping is a fluctuating pair density wave, but no microscopic model has yet been found which supports such a state. In this work, we write an analytically solvable model to examine pairing phases in the strongly coupled regime and in the presence of anisotropic interactions. Already for moderate coupling we find an unusual finite temperature phase, below an instability temperature Ti, where local pair correlations have non-zero center-of-mass momentum but lack long-range order. At low temperature, this fluctuating pair density wave can condense either to a uniform d-wave superconductor or the widely postulated pair-density wave phase depending on the interaction strength. Our minimal model offers a unified framework to understand the emergence of both fluctuating and long range pair density waves in realistic systems.

Effective doping and suppression of Fermi surface reconstruction via Fe vacancy disorder in K(x)Fe(2-y)Se2.

We investigate the effect of disordered vacancies on the normal-state electronic structure of the newly discovered alkali-intercalated iron selenide superconductors. To this end, we use a recently developed Wannier function based method to calculate from first principles the configuration-averaged spectral function of K0.8Fe1.6Se2 with disordered Fe and K vacancies. We find that the disorder can suppress the expected Fermi surface reconstruction without completely destroying the Fermi surface. More interestingly, the disorder effect raises the chemical potential significantly, giving enlarged electron pockets similar to highly doped KFe2Se2, without adding carriers to the system.

Creating superconductivity in WB2 through pressure-induced metastable planar defects.

High-pressure electrical resistivity measurements reveal that the mechanical deformation of ultra-hard WB2 during compression induces superconductivity above 50 GPa with a maximum superconducting critical temperature, Tcof 17 K at 91 GPa. Upon further compression up to 187 GPa, the Tcgradually decreases. Theoretical calculations show that electron-phonon mediated superconductivity originates from the formation of metastable stacking faults and twin boundaries that exhibit a local structure resembling MgB2 (hP3, space group 191, prototype AlB2). Synchrotron x-ray diffraction measurements up to 145 GPa show that the ambient pressure hP12 structure (space group 194, prototype WB2) continues to persist to this pressure, consistent with the formation of the planar defects above 50 GPa. The abrupt appearance of superconductivity under pressure does not coincide with a structural transition but instead with the formation and percolation of mechanically-induced stacking faults and twin boundaries. The results identify an alternate route for designing superconducting materials.

Evolution of the superconducting state of Fe-based compounds with doping.

We introduce an effective low-energy pairing model for Fe-based superconductors with s- and d-wave interaction components and a small number of input parameters and use it to study the doping evolution of the symmetry and the structure of the superconducting gap. We argue that the model describes the entire variety of pairing states found so far in the Fe-based superconductors and allows one to understand the mechanism of the attraction in s(±) and d(x(2)-y(2)) channels, the competition between s- and d-wave solutions, and the origin of superconductivity in heavily doped systems, when only electron or only hole pockets are present.