Crossover from weak to strong pairing in unconventional superconductors
D. S. Inosov, J. T. Park, A. Charnukha, Yuan Li, A. V. Boris, B. Keimer, V. Hinkov
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15 pages, 3 figures, 5 tables with an exhaustive overview of the published gap and spin-resonance measurements in Fe-based superconductors. New in V3: updated references. To be published in Phys. Rev. B
Superconductors are classified by their pairing mechanism and the coupling strength, measured as the ratio of the energy gap to the critical temperature, Tc. We present an extensive comparison of the gap ratios among many single- and multiband superconductors from simple metals to high-Tc cuprates and iron pnictides. Contrary to the recently suggested universality of this ratio in Fe-based superconductors, we find that the coupling in pnictides ranges from weak, near the BCS limit, to strong, as in cuprates, bridging the gap between these two extremes. Moreover, for Fe- and Cu-based materials, our analysis reveals a universal correlation between the gap ratio and Tc, which is not found in conventional superconductors and therefore supports a common unconventional pairing mechanism in both families. An important consequence of this result for ferropnictides is that the separation in energy between the excitonic spin-resonance mode and the particle-hole continuum, which determines the resonance damping, no longer appears independent of Tc.
On the assumption that two electrons with the same group velocity effectively attract each other a simple model Hamiltonian is proposed to question the existence of unconventional electron pairs formed by electrons in a strong periodic potential.
Non-magnetic impurities can lift the accidental degeneracy of unconventional pairing states, such as the $(d + i g)$-wave state recently proposed for Sr$_2$RuO$_4$. This type of effect would lead to a superconducting double transition upon impurity doping. In a model calculation it is shown how this behavior depends on material parameters and how it could be detected.
Giant and nil proximity effects and unconventional symmetry of cuprate superconductors are explained as a result of the strong Froehlich interaction of holes with c-axis polarised optical phonons acting together with an anisotropic nonlocal deformation potential.
We rigorously prove that an extended Hubbard model with attraction in two dimensions has an unconventional pairing ground state for any electron filling. The anisotropic spin-0 or anisotropic spin-1 pairing symmetry is realized, depending on a phase parameter characterizing the type of local attractive interactions. In both cases the ground state is unique. It is also shown that in a special case, where there are no electron hopping terms, the ground state has Ising-type Néel order at half-filling, when on-site repulsion is furthermore added. Physical applications are mentioned.
The pairing mechanism in A$_3$C$_{60}$ is investigated by studying the properties of a three-orbital Hubbard model with antiferromagnetic Hund coupling in the normal and superconducting phase. Local orbital fluctuations are shown to be substantially enhanced in the superconducting state, with a fluctuation energy scale that matches the low-energy peak in the spectral weight of the order parameter. Our results demonstrate that local orbital fluctuations provide the pairing glue in strongly correlated fulleride superconductors and support the spin/orbital freezing theory of unconventional superc…
The common wisdom that the phonon mechanism of electron pairing in the weak-coupling Bardeen-Cooper-Schrieffer (BCS) superconductors leads to conventional s-wave Cooper pairs is revised. An inevitable anisotropy of sound velocity in crystals makes the phonon-mediated attraction of electrons non-local in space providing unconventional Cooper pairs with a nonzero orbital momentum in a wide range of electron densities. As a result of this anisotropy quasi-two dimensional charge carriers undergo a quantum phase transition from an unconventional d-wave superconducting state to a conventional s-wave…
We use magnetic long range order as a tool to probe the Cooper pair wave function in the iron arsenide superconductors. We show theoretically that antiferromagnetism and superconductivity can coexist in these materials only if Cooper pairs form an unconventional, sign-changing state. The observation of coexistence in Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ then demonstrates unconventional pairing in this material. The detailed agreement between theory and neutron diffraction experiments, in particular for the unusual behavior of the magnetic order below $T_{c}$, demonstrates the robustness of our…
For a newly discovered iron-based high $T_c$ superconductor LaFeAsO$_{1-x}$F$_x$, we have constructed a minimal model, where inclusion of all the five Fe $d$ bands is found to be necessary. Random-phase approximation is applied to the model to investigate the origin of superconductivity. We conclude that the multiple spin fluctuation modes arising from the nesting across the disconnected Fermi surfaces realize an extended s-wave pairing, while d-wave pairing can also be another candidate.
We show that finite angular momentum pairing chiral superconductors on the triangular lattice have point zeroes in the complex gap function. A topological quantum phase transition takes place through a nodal superconducting state at a specific carrier density $x_c$ where the normal state Fermi surface crosses the isolated zeros. For spin singlet pairing, we show that the second nearest neighbor $d+id$-wave pairing can be the dominant pairing channel. The gapless critical state at $x_c\simeq0.25$ has six Dirac points and is topologically nontrivial with a $T^3$ spin relaxation rate below $T_c$.…
Recently synthesized Kagome compounds AV$_3$Sb$_5$ attract great attention due to the unusual coexistence of the topology, charge density wave and superconductivity. In this {\it Letter}, based on the band structures for CsV$_3$Sb$_5$ in pristine phase, we fit an effective 6-band model for the low-energy processes; utilizing the random phase approximation (RPA) on the effective minimal model, we obtain the momentum-resolved static spin susceptibility attributing the spin-fluctuation pairing mechanism, we find that the superconducting pairing strengths increase with the lift of the Coulomb corr…
A major question in Fe-based superconductors remains the structure of the pairing, in particular whether it is of unconventional nature. The electronic structure near vortices can serve as a platform for phase-sensitive measurements to answer this question. By solving Bogoliubov-de Gennes equations for LiFeAs, we calculate the energy-dependent local electronic structure near a vortex for different nodeless gap-structure possibilities. At low energies, the local density of states (LDOS) around a vortex is determined by the normal-state electronic structure. However, at energies closer to the ga…
This Letter theoretically discusses quasiparticle states and nuclear spin relaxation rates $T_1^{-1}$ in a quasi-one-dimensional superconductor (TMTSF)$_2$PF$_6$ under a magnetic field applied parallel to the conduction chains. We study the effects of Josephson-type vortices on $T_1^{-1}$ by solving the Bogoliubov de Gennes equation for $p$-, $d$- or $f$-wave pairing interactions. In the presence of line nodes in pairing functions, $T_1^{-1}$ is proportional to $T$ in sufficiently low temperatures because quasiparticles induced by vortices at the Fermi energy relax spins. We also try to identi…
Possibility of unconventional pairing due to Coulomb interaction in iron-pnictide superconductors is studied by applying a perturbative approach to realistic 2- and 5-band Hubbard models. The linearized Eliashberg equation is solved by expanding the effective pairing interaction perturbatively up to third order in the on-site Coulomb integrals. The numerical results for the 5-band model suggest that the eigenvalues of the Eliashberg equation are sufficiently large to explain the actual high Tc for realistic values of Coulomb interaction and the most probable pairing state is spin-singlet s-wav…
Superconductors with unconventional pairings have been a fascinating subject of research, for which a central issue is to explore effects that can be used to characterize the pairing. The process of Andreev reflection--the reflection of an electron as a hole at a normal-mental-superconductor interface by transferring a Cooper pair into the superconductor--offers a basic mechanism to probe the pairing through transport. Here we predict that in Andreev reflection from unconventional superconductors, the reflected hole acquires an anomalous spatial shift normal to the plane of incidence, arising …
We consider fermions on a 2D square lattice with a finite-range pairing interaction, and obtain signatures for unconventional pair-symmetry states, $d_{x^2-y^2}$ and extended-s ($s^*$), in the BCS-BEC crossover region. We find that the fermion momentum distribution function, $v_k^2$, the ratio of the Bogoliubov coefficients, $v_k/u_k$, and the Fourier transform of $v_k^2$ are strikingly different for $d$- and $s^*$ symmetries in the crossover region. The chemical potential and the gaps functions for both pairing symmetries show several interesting features as a function of interaction. Fermion…
Cuprates and iron-based superconductors are two classes of unconventional high Tc superconductors based on 3d transition elements. Recently, two principles, correspondence principle and magnetic selective pairing rule, have been emerged to unify their high Tc superconducting mechanisms. These principles strongly regulate electronic structures that can host high Tc superconductivity. Guided by these principles, here we propose high Tc superconducting candidates that are formed by cation-anion trigonal bipyramidal complexes with a d^7 filling configuration on the cation ions. Their superconducti…
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…
To pinpoint the microscopic mechanism for superconductivity has proven to be one of the most outstanding challenges in the physics of correlated quantum matter. Thus far, the most direct evidence for an electronic pairing mechanism is the observation of a new symmetry of the order-parameter, as done in the cuprate high-temperature superconductors. Like distinctions based on the symmetry of a locally defined order-parameter, global, topological invariants allow for a sharp discrimination between states of matter that cannot be transformed into each other adiabatically. Here we propose an unconv…
UCoGe is reported as a weak ferromagnetic (FM) two-band superconductor (SC) with the critical temperature, $T_{\mathrm{SC}}\sim$ 0.7 K and the Curie temperature, $T_{\mathrm{C}}\sim$ 3 K at ambient pressure. We report exotic attributes of the SC and FM state in moderate magnetic fields. The observed phenomena clearly demonstrate that the SC regime is superior to the paramagnetic state in the vicinity of $T_{\mathrm{SC}}$. Above $T_{\mathrm{SC}}$, the zero-field state is characterized by a regime with strong FM spin fluctuations, suggesting proximity of the FM quantum critical point (FM-QCP). I…
We study the phase diagram in a two-dimensional Fermi gas with the synthetic spin-orbit coupling that has recently been realized experimentally. In particular, we characterize in detail the properties and the stability region of the unconventional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in such a system, which are induced by spin-orbit coupling and Fermi surface asymmetry. We identify several distinct nodal FFLO states by studying the topology of their respective gapless contours in momentum space. We then examine the phase structure and the number density distributions in a typical har…
We study superfluid properties of fermions on a 2D lattice using a finite-range pairing interaction derivable from an extended Hubbard model. We obtain signatures of unconventional pair-symmetry states, $d_{x^2-y^2}$ and extended-s ($s^*$), in the BCS-BEC crossover region. The fermion momentum distribution function, $v_k^2$, the ratio of the Bogoliubov coefficients, $v_k/u_k$, and the Fourier transform of $v_k^2$ are among the properties that are strikingly different for d- and $s^*$ symmetries in the crossover region. Fermionic atoms in 2D optical lattices may provide a way to observe these s…
The recent discovery of AV$_3$Sb$_5$ (A=K,Rb,Cs) has uncovered an intriguing arena for exotic Fermi surface instabilities in a kagome metal. Among them, superconductivity is found in the vicinity of multiple van Hove singularities, exhibiting indications of unconventional pairing. We show that the sublattice interference mechanism is central to understanding the formation of superconductivity in a kagome metal. Starting from an appropriately chosen minimal tight-binding model with multiple with multiple van Hove singularities close to the Fermi level for AV$_3$Sb$_5$, we provide a random phase…
The exact numerical diagonalization and thermodynamics in an ensemble of small Hubbard clusters in the ground state and finite temperatures reveal intriguing insights into the nascent charge and spin pairings, Bose condensation and ferromagnetism in nanoclusters. The phase diagram off half filling strongly suggests the existence of subsequent transitions from electron pairing into unsaturated and saturated ferromagnetic Mott-Hubbard like insulators, driven by electron repulsion. Rigorous criteria for the existence of quantum critical points in the ground state and corresponding crossovers at f…
The Fermi-liquid theory of superconductivity is applicable to a broad range of systems that are candidates for unconventional pairing. Fundamental differences between unconventional and conventional anisotropic superconductors are illustrated by the unique effects that impurities have on the low-temperature transport properties of unconventional superconductors. For special classes of unconventional superconductors the low-temperature transport coefficients are {\it universal}, i.e. independent of the impurity concentration and scattering phase shift. The existence of a universal limit depends…
We study the one-dimensional attractive Fermionic Hubbard model under the influence of periodic driving with the time-dependent density matrix renormalization group method. We show that the system can be driven into an unconventional pairing state characterized by a condensate made of Cooper-pairs with a finite center-of-mass momentum similar to a Fulde-Ferrell state. We obtain results both in the laboratory and the rotating reference frames demonstrating that the momentum of the condensate can be finely tuned by changing the ratio between the amplitude and the frequency of the driving. In par…
Unconventional superconductivity is usually associated with symmetry breaking in the system. Here we consider a simple setup consisting of a solid state material with conduction electrons and an applied surface acoustic wave (SAW), that can break time and spatial translation symmetries. We study the symmetries of the possible SAW-induced order parameters, showing that even-frequency spin-triplet odd-parity order parameter can occur. We suggest different methods of how to engineer the symmetries of the order parameters using SAWs and the applications of such setups.
In this letter, we have examined the superconducting ground state of the HfV$_2$Ga$_4$ compound using resistivity, magnetization, zero-field (ZF) and transverse-field (TF) muon-spin relaxation and rotation ($μ$SR) measurements. Resistivity and magnetization unveil the onset of bulk superconductivity with $T_{\bf c}\sim$ 3.9~K, while TF-$μ$SR measurements show that the temperature dependence of the superfluid density is well described by a nodal two-gap $s$+$d$-wave order parameter model. In addition, ZF muon relaxation rate increases with decreasing temperature below 4.6 K, indicating the pres…
High-Tc superconductivity in layered cuprates is described in a BCS-BEC formalism with linearly-dispersive s- and d-wave Cooper pairs moving in quasi-2D finite-width layers about the CuO_2 planes. This yields a closed formula for Tc determined by the layer width, the Debye frequency, the pairing energy, and the in-plane penetration depth. The new formula reasonably reproduces empirical values of superconducting Tc's for seven different compounds among the LSCO, YBCO, BSCCO and TBCCO layered cuprates.
Various mechanisms have been put forward for cuprate superconductivity, which fit largely into two camps: spin-fluctuation and electron-phonon (el-ph) mechanisms. However, in spite of a large effort, electron-phonon interactions are not fully understood away from clearly defined limits. To this end, we use a numerically exact algorithm to simulate the binding of bipolarons. We present the results of a continuous-time quantum Monte-Carlo (CTQMC) algorithm on a tight-binding lattice, for bipolarons with arbitrary interaction range in the presence of strong coulomb repulsion. The algorithm is suf…
Fingerprints of unconventional pairing in superconductor-hole-gas heterostructures
Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所）；Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所）；Department of Physics, Norwegian University of Science and Technology（挪威科技大学物理系）
The structures, the phase diagrams, and the appearance of a neutron resonance signaling an unconventional superconducting state provide phenomenological evidence relating the cuprates, the Fe-pnictides/chalcogenides as well as some heavy fermion and actinide materials. Single- and multi-band Hubbard models have been found to describe a number of the observed properties of these materials so that it is reasonable to examine the origin of the pairing interaction in these models. In this review, based on the experimental phenomenology and studies of the pairing interaction for Hubbard-like models…
One of the major themes in the physics of condensed matter is unconventional superconductivity in correlated electronic systems. The symmetry structure of Cooper pairs is thought to be the key to the understanding of the pairing mechanism of their superconductivity. In iron pnictide superconductors, the precise symmetry of the order parameter as well its evolution with doping remains highly controversial. There is no general consensus on the nature of pairing in iron-based superconductors leaving the perspectives ranging from $s^{++}$ wave, to $s^{\pm}$, and $d$ wave. Here we show that doping …
We study the pairing symmetry of a doped Kane-Mele model on a honeycomb lattice with on-site Coulomb interaction. The pairing instability of Cooper pair is calculated based on the linearized Eliashberg equation within the random phase approximation (RPA). When the magnitude of the spin-orbit coupling is weak, even-frequency spin-singlet even-parity (ESE) pairing is dominant. On the other hand, with the increase of the spin-orbit coupling, we show that the even-frequency spin-triplet odd-parity (ETO) f-wave pairing exceeds ESE one. ETO f-wave pairing is supported by the longitudinal spin fluctu…
The pairing mechanism in iron-based superconductors is believed to be unconventional, i.e. not phonon-mediated. The achieved transition temperatures Tc in these superconductors are still significantly below those of some of the cuprates, with the exception of single layer FeSe films on SrTiO3 showing a Tc between 60 and 100 K, i.e. an order of magnitude larger than in bulk FeSe. This enormous increase of Tc demonstrates the potential of interface engineering for superconductivity, yet the underlying mechanism of Cooper pairing is not understood. Both conventional and unconventional mechanisms …
We investigate the superconductivity in the $t-J-U$ model within a slave-spin formalism. We show that the BCS mean-field theory implemented with the slave spin formalism naturally predicts two distinct gaps which are the pairing gap of the spinons $Δ_f$ and the Cooper pairing gap of the electrons $Δ_{SC} = ZΔ_f$, where $Z$ is the quasiparticle weight. Furthermore, we find that the nature of the superconducting state depends crucially on the interaction providing the pairing mechanism. For spin interactions, the bandwidth of the spinon hopping term is renormalized by $Z$ but the its pairing ter…
We have demonstrated that it is possible to access a crossover scenario starting with a weak coupling (BCS) d-wave superconductor to a strongly coupled Bose-Einstein condensate (BEC) phase as the exchange interaction is tuned in a two dimensional system described by a t-J-U model via numerically solving the Bogoliubov-de Gennes (BdG) equations. While in the extreme dilute limit, the electronic pairing phenomena is independent of the Coulomb repulsion, U, the superconductivity depends on U, and so does the crossover. Further, the effect of variation in the carrier density on the BCS-BEC crossov…
We propose a mechanism whereby disorder can enhance the transition temperature Tc 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 …
The rapid experimental progress of ultra-cold dipolar fermions opens up a whole new opportunity to investigate novel many-body physics of fermions. In this article, we review theoretical studies of the Fermi liquid theory and Cooper pairing instabilities of both electric and magnetic dipolar fermionic systems from the perspective of unconventional symmetries. When the electric dipole moments are aligned by the external electric field, their interactions exhibit the explicit $d_{r^2-3z^2}$ anisotropy. The Fermi liquid properties, including the single-particle spectra, thermodynamic susceptibili…
For the iron-based high $T_c$ superconductor LaFeAsO$_{1-x}$F$_x$, we construct a minimal model, where all of the five Fe $d$ bands turn out to be involved. We then investigate the origin of superconductivity with a five-band random-phase approximation by solving the Eliashberg equation. We conclude that the spin fluctuation modes arising from the nesting between the disconnected Fermi pockets realise, basically, an extended s-wave pairing, where the gap changes sign across the nesting vector.
In a recent work by Schrodi $\textit{et al}$. [Phys. Rev. B. $\textbf{104}$, L140506 (2021)], the authors find an unconventional superconducting state with a sign-changing order parameter using the Migdal-Eliashberg theory, including the first vertex correction. This unconventional solution arises despite using an isotropic bare electron-phonon coupling in the Hamiltonian. We examine this claim using hybrid quantum Monte Carlo for a single-band Holstein model with a cuprate-like noninteracting band structure and identical parameters to Schrodi $\textit{et al}$.. Our Monte Carlo results for the…
It has gone almost unquestioned that superexchange in the t-J (or Hubbard) model, and not phonons, is responsible for the unconventional ("d-wave") pairing symmetry of cuprate superconductors. However a number of advanced numerical studies have not found superconductivity in the Hubbard model. On the other hand compelling experimental evidence for a strong electron-phonon interaction (EPI) has currently arrived. Here I briefly review some phonon-mediated unconventional pairing mechanisms. In particular the anisotropy of sound velocity makes the phonon-mediated attraction of electrons non-local…
Cooper pairs in two-dimensional unconventional superconductors with broken inversion symmetry are in a mixture of an even-parity spin-singlet pairing state with an odd-parity spin-triplet pairing state. We study the magnetic properties of the impurity bound states in such superconductors and find striking signatures in their spin polarization which allow to unambiguously discriminate a non-topological superconducting phase from a topological one. Moreover, we show how these properties, which could be measured using spin-polarized scanning tunneling microscopy (STM), also enable to determine th…
A general phenomenological theory is presented for the phase behavior of ferromagnetic superconductors with spin-triplet electron Cooper pairing. The theory describes in details the temperature-pressure phase diagrams of real inter-metallic compounds exhibiting the remarkable phenomenon of coexistence of spontaneous magnetic moment of the itinerant electrons and spin-triplet superconductivity. The quantum phase transitions which may occur in these systems are also described. The theory allows for a classification of these itinerant ferromagnetic superconductors in two types: type I and type II…
We have investigated the proximity effect in superconductor/ferromagnet junctions in a systematic manner to discuss the relationship between the zero-energy peak (ZEP) of the local density of states (LDOS) and spin-triplet odd-frequency pairing. By exactly solving the nonlinear Usadel equations, we have found that the ZEP is realized in a wide range of geometrical and material parameters in the case of the noncollinear magnetization. This strongly suggests the robustness of the ZEP induced by spin-triplet odd-frequency pairing in such systems. We also found that the crossover from singlet pair…
We suggest a new family of Co/Ni-based materials that may host unconventional high temperature superconductivity (high-T$_c$). These materials carry layered square lattices with each layer being formed by vertex-shared transition metal tetrahedra cation-anion complexes. The electronic physics in these materials is determined by the two dimensional layer and is fully attributed to the three near degenerated $t_{2g}$ d-orbitals close to a $d^7$ filling configuration in the d-shell of Co/Ni atoms . The electronic structure meets the necessary criteria for unconventional high T$_c$ materials propo…
Based on an effective two-band model and using the fluctuation-exchange (FLEX) approach, we explore spin fluctuations and unconventional superconducting pairing in Fe-based layer superconductors. It is elaborated that one type of interband antiferromagnetic (AF) spin fluctuation stems from the interband Coulomb repulsion, while the other type of intraband AF spin fluctuation originates from the intraband Coulomb repulsion. Due to the Fermi-surface topology, a spin-singlet extended s-wave superconducting state is more favorable than the nodal $d_{XY}$-wave state if the interband AF spin fluctua…
We report observation of the nonlinear Meissner effect (NLME) in Nb films by measuring the resonance frequency of a planar superconducting cavity as a function of the magnitude and the orientation of a parallel magnetic field. Use of low power rf probing in films thinner than the London penetration depth, significantly increases the field for the vortex penetration onset and enables NLME detection under true equilibrium conditions. The data agree very well with calculations based on the Usadel equations. We propose to use NLME angular spectroscopy to probe unconventional pairing symmetries in …
The exceptionally low-symmetry crystal structures of the time-reversal symmetry breaking superconductors LaNiC$_2$ and LaNiGa$_2$ lead to an internally-antisymmetric non-unitary triplet (INT) state as the only possibility compatible with experiments. We argue that this state has a distinct signature: a double-peak structure in the Density of States (DOS) which resolves in the spin channel in a particular way. We construct a detailed model of LaNiGa$_2$ capturing its electronic band structure and magnetic properties ab initio. The pairing mechanism is described via a single adjustable parameter…
To shed light on the symmetry of the superconducting order parameter in Na_xCoO_2-yH_2O, the Mn doping effects are studied. X-ray absorption spectroscopy verifies that the doped Mn impurities occupy the Co sites and are with a valance close to +4. Impurity scattering by Mn is in the unitary limit that, however, does not lead to strong Tc suppression. This absence of the strong impurity effects on T_c is not consistent with the simple picture of a sign-changing order parameter. Coexistence of the s-wave and unconventional order parameters is proposed to reconcile all existing experiments and ha…
The origin of Cooper pairing in high-temperature superconductors, such as the copper-oxide and iron-based system, is still under debate. High transition temperatures together with unconventional pairing states support the picture of an electronic pairing glue in the cuprates, where superconductivity is mediated by collective bosonic excitations of the electron fluid. In other materials, most importantly iron based systems with only hole or only electron pockets, the microscopic origin is hotly debated. Scanning tunneling microscopy (STM) has been shown to be a powerful experimental probe to de…
