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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. The progress and the outstanding issues in understanding the correlated phases in the unconventional iron-based superconductors is reviewed.

Motivated by the recently discovered high- T c superconductor La 3 Ni 2 O 7 , we comprehensively study this system using density functional theory and random phase approximation calculations. At low pressures, the Amam phase is stable, containing the Y 2− mode distortion from the Fmmm phase, while the Fmmm phase is unstable. Because of small differences in enthalpy and a considerable Y 2− mode amplitude, the two phases may coexist in the range between 10.6 and 14 GPa, beyond which the Fmmm phase dominates. In addition, the magnetic stripe-type spin order with wavevector ( π , 0) was stable at the intermediate region. Pairing is induced in the s ± -wave channel due to partial nesting between the M  = ( π ,  π ) centered pockets and portions of the Fermi surface centered at the X  = ( π , 0) and Y  = (0,  π ) points. This resembles results for iron-based superconductors but has a fundamental difference with iron pnictides and selenides. Moreover, our present efforts also suggest La 3 Ni 2 O 7 is qualitatively different from infinite-layer nickelates and cuprate superconductors. Recently superconductivity with T c of about 80 K was discovered in a bilayer nickelate La 3 Ni 2 O 7 under high pressure. Here the authors report a density functional theory and random phase approximation study of structural and electronic properties as a function of pressure and discuss the pairing mechanism.

The interactions that lead to the emergence of superconductivity in iron-based materials remain a subject of debate. It has been suggested that electron-electron correlations enhance electron-phonon coupling in iron selenide (FeSe) and related pnictides, but direct experimental verification has been lacking. Here we show that the electron-phonon coupling strength in FeSe can be quantified by combining two time-domain experiments into a “coherent lock-in” measurement in the terahertz regime. X-ray diffraction tracks the light-induced femtosecond coherent lattice motion at a single phonon frequency, and photoemission monitors the subsequent coherent changes in the electronic band structure.Comparison with theory reveals a strong enhancement of the coupling strength in FeSe owing to correlation effects. Given that the electron-phonon coupling affects superconductivity exponentially, this enhancement highlights the importance of the cooperative interplay between electron-electron and electron-phonon interactions.

The pair density wave (PDW) is a superconducting state in which Cooper pairs carry centre-of-mass momentum in equilibrium, leading to the breaking of translational symmetry 1 – 4 . Experimental evidence for such a state exists in high magnetic field 5 – 8 and in some materials that feature density-wave orders that explicitly break translational symmetry 9 – 13 . However, evidence for a zero-field PDW state that exists independent of other spatially ordered states has so far been elusive. Here we show that such a state exists in the iron pnictide superconductor EuRbFe 4 As 4 , a material that features co-existing superconductivity (superconducting transition temperature ( T c ) ≈ 37 kelvin) and magnetism (magnetic transition temperature ( T m ) ≈ 15 kelvin) 14 , 15 . Using spectroscopic imaging scanning tunnelling microscopy (SI-STM) measurements, we show that the superconducting gap at low temperature has long-range, unidirectional spatial modulations with an incommensurate period of about eight unit cells. Upon increasing the temperature above T m , the modulated superconductor disappears, but a uniform superconducting gap survives to T c . When an external magnetic field is applied, gap modulations disappear inside the vortex halo. The SI-STM and bulk measurements show the absence of other density-wave orders, indicating that the PDW state is a primary, zero-field superconducting state in this compound. Both four-fold rotational symmetry and translation symmetry are recovered above T m , indicating that the PDW is a smectic order. Measurements show that smectic pair-density-wave order exists in the magnetic iron pnictide superconductor EuRbFe 4 As 4 and that the pair-density-wave state is a primary, zero-field superconducting state in this compound.

Iron-chalcogenide superconductors have emerged as a promising Majorana platform for topological quantum computation. By combining topological band and superconductivity in a single material, they provide significant advantage to realize isolated Majorana zero modes. However, iron-chalcogenide superconductors, especially Fe(Te,Se), suffer from strong inhomogeneity which may hamper their practical application. In addition, some iron-pnictide superconductors have been demonstrated to have topological surface states, yet no Majorana zero mode has been observed inside their vortices, raising a question of universality about this new Majorana platform. In this work, through angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy measurement, we identify Dirac surface states and Majorana zero modes, respectively, for the first time in an iron-pnictide superconductor, CaKFe 4 As 4 . More strikingly, the multiple vortex bound states with integer-quantization sequences can be accurately reproduced by our model calculation, firmly establishing Majorana nature of the zero mode. Iron-pnictide superconductors share similar topological band structure with iron-chalcogenide superconductors, but no Majorana modes have been observed in the former. Here, the authors observe both the superconducting Dirac surface states and Majorana zero modes inside its vortex cores in CaKFe 4 As 4 .

Nontrivial topology and unconventional pairing are two central guiding principles in the contemporary search for and analysis of superconducting materials and heterostructure compounds. Previously, a topological superconductor has been predominantly conceived to result from a topologically nontrivial band subject to an intrinsic or external superconducting proximity effect. Here, we propose a new class of topological superconductors that are uniquely induced by unconventional pairing. They exhibit a boundary-obstructed higher-order topological character and, depending on their dimensionality, feature unprecedently robust Majorana bound states or hinge modes protected by chiral symmetry. We predict the 112 family of iron pnictides, such asCa1−xLaxFeAs2, to be highly suited material candidates for our proposal, which can be tested by edge spectroscopy. Because of the boundary obstruction, the topologically nontrivial feature of the 112 pnictides does not reveal itself for a bulk-only torus band analysis without boundaries, and as such, it had evaded previous investigations. Our proposal not only opens a new arena for highly stable Majorana modes in high-temperature superconductors but also provides the smoking gun for extendeds-wave order in the iron pnictides.

In general, magnetism and superconductivity are antagonistic to each other. However, there are several families of superconductors in which superconductivity coexists with magnetism, and a few examples are known where the superconductivity itself induces spontaneous magnetism. The best known of these compounds are Sr 2 RuO 4 and some non-centrosymmetric superconductors. Here, we report the finding of a narrow dome of an s + i s ′ superconducting phase with apparent broken time-reversal symmetry (BTRS) inside the broad s -wave superconducting region of the centrosymmetric multiband superconductor Ba 1 −  x K x Fe 2 As 2 (0.7 ≲  x  ≲ 0.85). We observe spontaneous magnetic fields inside this dome using the muon spin relaxation (μSR) technique. Furthermore, our detailed specific heat study reveals that the BTRS dome appears very close to a change in the topology of the Fermi surface. With this, we experimentally demonstrate the likely emergence of a novel quantum state due to topological changes of the electronic system. An exotic s  +  is multiband superconducting state manifests in a doped pnictide superconductor when a second band moves below the Fermi surface. This creates an internal magnetic field, breaking time-reversal symmetry.

A systematic spectroscopic analysis of the principal members of the iron pnictide family of superconductors reveals a substantial spin–orbit splitting. Spin–orbit coupling is a fundamental interaction in solids that can induce a broad range of unusual physical properties, from topologically non-trivial insulating states to unconventional pairing in superconductors 1 , 2 , 3 , 4 , 5 , 6 , 7 . In iron-based superconductors its role has, so far, not been considered of primary importance, with models based on spin- or orbital fluctuations pairing being used most widely 8 , 9 , 10 . Using angle-resolved photoemission spectroscopy, we directly observe a sizeable spin–orbit splitting in all the main members of the iron-based superconductors. We demonstrate that its impact on the low-energy electronic structure and details of the Fermi surface topology is stronger than that of possible nematic ordering 11 , 12 , 13 . The largest pairing gap is supported exactly by spin–orbit-coupling-induced Fermi surfaces, implying a direct relation between this interaction and the mechanism of high-temperature superconductivity.

Despite much theoretical effort, there is no complete theory of the “strange” metal state of the high temperature superconductors, and its linear-in-temperatureTresistivity. Recent experiments showing an unexpected linear-in-fieldBmagnetoresistivity have deepened the puzzle. We propose a simple model of itinerant electrons, interacting via random couplings, with electrons localized on a lattice of “quantum dots” or “islands.” This model is solvable in a particular large-Nlimit and can reproduce observed behavior. The key feature of our model is that the electrons in each quantum dot are described by a Sachdev-Ye-Kitaev model describing electrons without quasiparticle excitations. For a particular choice of the interaction between the itinerant and localized electrons, this model realizes a controlled description of a diffusive marginal-Fermi liquid (MFL) without momentum conservation, which has a linear-in-Tresistivity and aTlnTspecific heat asT→0. By tuning the strength of this interaction relative to the bandwidth of the itinerant electrons, we can additionally obtain a finite-Tcrossover to a fully incoherent regime that also has a linear-in-Tresistivity. We describe the magnetotransport properties of this model and show that the MFL regime has conductivities that scale as a function ofB/T; however, the magnetoresistance saturates at largeB. We then consider a macroscopically disordered sample with domains of such MFLs with varying densities of electrons and islands. Using an effective-medium approximation, we obtain a macroscopic electrical resistance that scales linearly in the magnetic fieldBapplied perpendicular to the plane of the sample, at largeB. The resistance also scales linearly inTat smallB, and asTf(B/T)at intermediateB. We consider implications for recent experiments reporting linear transverse magnetoresistance in the strange metal phases of the pnictides and cuprates.

Flat-band materials such as the kagome metals or moiré superlattices are of intense current interest. Flat bands can result from the electron motion on numerous (special) lattices and usually exhibit topological properties. Their reduced bandwidth proportionally enhances the effect of Coulomb interaction, even when the absolute magnitude of the latter is relatively small. Seemingly unrelated to these materials is the large family of strongly correlated electron systems, which include the heavy-fermion compounds, and cuprate and pnictide superconductors. In addition to itinerant electrons from large, strongly overlapping orbitals, they frequently contain electrons from more localized orbitals, which are subject to a large Coulomb interaction. The question then arises as to what commonality in the physical properties and microscopic physics, if any, exists between these two broad categories of materials. A rapidly increasing body of strikingly similar phenomena across the different platforms — from electronic localization–delocalization transitions to strange-metal behaviour and unconventional superconductivity — suggests that similar underlying principles could be at play. Indeed, it has recently been suggested that flat-band physics can be understood in terms of Kondo physics. Inversely, the concept of electronic topology from lattice symmetry, which is fundamental in flat-band systems, is enriching the field of strongly correlated electron systems, in which correlation-driven topological phases are increasingly being investigated. In this Perspective article, we elucidate this connection, survey the new opportunities for cross-fertilization across platforms and assess the prospect for new insights that may be gained into correlation physics and its intersection with electronic topology. Flat-band materials such as kagome and moiré lattices and strongly correlated electron systems including heavy-fermion compounds exhibit strikingly similar phenomena of topology and strong correlations. This Perspective article discusses Kondo physics as the underlying theme and a route to a unified understanding.