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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.

The nematic electronic state and its associated critical fluctuations have emerged as a potential candidate for the superconducting pairing in various unconventional superconductors. However, in most materials their coexistence with magnetically ordered phases poses a significant challenge in determining their importance. Here, by combining chemical and hydrostatic physical pressure in FeSe 0.89 S 0.11 , we access a nematic quantum phase transition isolated from any other competing magnetic phases. From quantum oscillations in high magnetic fields, we trace the evolution of the Fermi surface and electronic correlations as a function of applied pressure and detect a Lifshitz transition that separates two distinct superconducting regions. One emerges from the nematic phase with a small Fermi surface and strong electronic correlations, while the other one has a large Fermi surface and weak correlations that promotes nesting and stabilization of a magnetically ordered phase at high pressures. The absence of mass divergence at the nematic quantum phase transition suggests that the nematic fluctuations could be quenched by the strong coupling to the lattice or local strain effects. A direct consequence is the weakening of superconductivity at the nematic quantum phase transition in the absence of magnetically driven fluctuations. Using sulfur doping and pressure, the authors separate the nematic and magnetic phase transitions in FeSe. They find that a Lifshitz transition sits between two independent superconducting domes where nematic critical fluctuations remain finite.

The magnetotransport behavior inside the nematic phase of bulk FeSe reveals unusual multiband effects that cannot be reconciled with a simple two-band approximation proposed by surface-sensitive spectroscopic probes. In order to understand the role played by the multiband electronic structure and the degree of two-dimensionality, we have investigated the electronic properties of exfoliated flakes of FeSe by reducing their thickness. Based on magnetotransport and Hall resistivity measurements, we assess the mobility spectrum that suggests an unusual asymmetry between the mobilities of the electrons and holes, with the electron carriers becoming localized inside the nematic phase. Quantum oscillations in magnetic fields up to 38 T indicate the presence of a hole-like quasiparticle with a lighter effective mass and a quantum scattering time three times shorter, as compared with bulk FeSe.The observed localization of negative charge carriers by reducing dimensionality can be driven by orbitally dependent correlation effects, enhanced interband spin fluctuations, or a Lifshitz-like transition, which affect mainly the electron bands. The electronic localization leads to a fragile two-dimensional superconductivity in thin flakes of FeSe, in contrast to the two-dimensional high-T c induced with electron doping via dosing or using a suitable interface.

FeSe is a unique superconductor that can be manipulated to enhance its superconductivity using different routes, while its monolayer form grown on different substrates reaches a record high temperature for a two-dimensional system. In order to understand the role played by the substrate and the reduced dimensionality on superconductivity, we examine the superconducting properties of exfoliated FeSe thin flakes by reducing the thickness from bulk down towards 9 nm. Magnetotransport measurements performed in magnetic fields up to 16 T and temperatures down to 2 K help to build up complete superconducting phase diagrams of different thickness flakes. While the thick flakes resemble the bulk behaviour, by reducing the thickness the superconductivity of FeSe flakes is suppressed. The observation of the vortex-antivortex unbinding transition in different flakes provide a direct signature of a dominant two-dimensional pairing channel. However, the upper critical field reflects the evolution of the multi-band nature of superconductivity in FeSe becoming highly two-dimensional and strongly anisotropic only in the thin limit. Our study provides detailed insights into the evolution of the superconducting properties of a multi-band superconductor FeSe in the thin limit in the absence of a dopant substrate.

In the Kitaev honeycomb model, spins coupled by strongly-frustrated anisotropic interactions do not order at low temperature but instead form a quantum spin liquid with spin fractionalisation into Majorana fermions and static fluxes. The realization of such a model in crystalline materials could lead to major breakthroughs in understanding entangled quantum states, however achieving this in practice is a very challenging task. The recently synthesized honeycomb material RuI 3 shows no long-range magnetic order down to the lowest probed temperatures and has been theoretically proposed as a quantum spin liquid candidate material on the verge of an insulator to metal transition. Here we report a comprehensive study of the magnetic anisotropy in un-twinned single crystals via torque magnetometry and detect clear signatures of strongly anisotropic and frustrated magnetic interactions. We attribute the development of sawtooth and six-fold torque signal to strongly anisotropic, bond-dependent magnetic interactions by comparing to theoretical calculations. As a function of magnetic field strength at low temperatures, torque shows an unusual non-parabolic dependence suggestive of a proximity to a field-induced transition. Thus, RuI 3 , without signatures of long-range magnetic order, displays key hallmarks of an exciting candidate for extended Kitaev magnetism with enhanced quantum fluctuations. Quantum spin liquids are materials predicted to be absent of magnetic ordering at low temperature, giving rise to fractionalised electronic states, but conclusive experimental evidence is still absent. Here, the authors conduct angular dependent torque measurements on the candidate spin liquid material RuI3 and, through a comparison of experimental and theoretical results, provide evidence indicating the presence of frustrated magnetic interactions in the system.

In 2008, new classes of high-temperature superconductors containing iron have been discovered. These iron pnictides offer a new area of exploration and understanding of superconductivity. Quantum oscillations is a bulk probe that allows us to map out the full Fermi surface of a superconducting system in its normal metallic state. These oscillations are determined by the Landau quantization in high magnetic fields and are usually observed at very low temperatures and in very clean samples. By knowing the exact nature of the quasi-particles in the normal state and the degree of electronic correlations, one can simplify and restrict theoretical models required to understand the pairing mechanism in superconductors. I will discuss the current understanding of the Fermi surface studies in iron-based superconductors as determined from quantum oscillations.

The existence of a nematic phase transition in iron-chalcogenide superconductors poses an intriguing question about its impact on superconductivity. To understand the nature of this unique quantum phase transition, it is essential to study how the electronic structure changes across this transition at low temperatures. Here, we investigate the evolution of the Fermi surfaces and electronic interactions across the nematic phase transition of FeSe1−xSx using Shubnikov-de Haas oscillations in high magnetic fields up to 45 T in the low temperature regime down to 0.4 K. Most of the Fermi surfaces of FeSe1−xSx monotonically increase in size except for a prominent low frequency oscillation associated with a small, but highly mobile band, which disappears at the nematic phase boundary near x ~ 0.17, indicative of a topological Lifshitz transition. The quasiparticle masses are larger inside the nematic phase, indicative of a strongly correlated state, but they become suppressed outside it. The experimentally observed changes in the Fermi surface topology, together with the varying degree of electronic correlations, will change the balance of electronic interactions in the multi-band system FeSe1−xSx and promote different kz-dependent superconducting pairing channels inside and outside the nematic phase.Fe-based superconductors: Characterizing the nematic phase transitionNew measurements of quantum oscillations in FeSe1-xSx help understanding the nature of the nematic phase transition in Fe-based superconductors. Nematic order — an electronic order that breaks the rotational symmetry of the underlying substrate — is thought to play an important role in the appearance of superconductivity in Fe-based superconductors. A way to investigate the interplay between nematicity and superconductivity is to apply chemical pressure, in this case by substituting Se with S in FeSe samples. Amalia Coldea from the University of Oxford, UK, and colleagues used Shubnikov-de Haas oscillations to characterize the evolution of the Fermi surfaces across the nematic phase transition. They found a strongly correlated state inside the nematic phase and weakening electronic correlations outside it, and evidence for a Lifshitz transition that had not been detected before.

We investigate the high-pressure phase of the iron-based superconductor FeSe0.89S0.11 using transport and tunnel diode oscillator studies using diamond anvil cells. We construct detailed pressure-temperature phase diagrams that indicate that the superconducting critical temperature is strongly enhanced by more than a factor of four towards 40 K above 4 GPa. The resistivity data reveal signatures of a fan-like structure of non-Fermi liquid behaviour which could indicate the existence of a putative quantum critical point buried underneath the superconducting dome around 4.3 GPa. With further increasing the pressure, the zero-field electrical resistivity develops a non-metallic temperature dependence and the superconducting transition broadens significantly. Eventually, the system fails to reach a fully zero-resistance state, and the finite resistance at low temperatures becomes strongly current-dependent. Our results suggest that the high-pressure, high-Tc phase of iron chalcogenides is very fragile and sensitive to uniaxial effects of the pressure medium, cell design and sample thickness. This high-pressure region could be understood assuming a real-space phase separation caused by nearly concomitant electronic and structural instabilities.

Iron-chalcogenide superconductors display rich phenomena caused by orbital-dependent band shifts and electronic correlations. Additionally, they are potential candidates for topological superconductivity due to the band inversion between the Fe d bands and the chalcogen p z band. Here we present a detailed study of the electronic structure of the nematic superconductors FeSe 1− x Te x (0 <  x  < 0.4) using angle-resolved photoemission spectroscopy to understand the role of orbital-dependent band shifts, electronic correlations and the chalcogen band. We assess the changes in the effective masses using a three-band low energy model, and the band renormalization via comparison with DFT band structure calculations. The effective masses decrease for all three-hole bands inside the nematic phase, followed by a strong increase for the band with d x y orbital character. Interestingly, this nearly-flat d x y band becomes more correlated as it shifts towards the Fermi level with increasing Te concentrations and as the second superconducting dome emerges. Our findings suggests that the d x y hole band, which is very sensitive to the chalcogen height, could be involved in promoting an additional pairing channel and increasing the density of states to stabilize the second superconducting dome in FeSe 1− x Te x . This simultaneous shift of the d x y hole band and enhanced superconductivity is in contrast with FeSe 1− x S x . The iron chalcogenide material FeSe1-xTex constitutes an important family of unconventional superconductors but its nematic phase was less explored due to a lack of single crystals. In this study, the authors provide a systematic study of the electronic structure for nematic FeSe1-xTex and observe that as the Te content increases a gradual shift and renormalization of the dxy orbital occurs, concomitant with the enhancement of superconductivity.

The nematic electronic state and its associated critical fluctuations have emerged as a potential candidate for the superconducting pairing in various unconventional superconductors. However, in most materials their coexistence with magnetically ordered phases poses a significant challenge in determining their importance. Here, by combining chemical and hydrostatic physical pressure in FeSe0.89S0.11, we access a nematic quantum phase transition isolated from any other competing magnetic phases. From quantum oscillations in high magnetic fields, we trace the evolution of the Fermi surface and electronic correlations as a function of applied pressure and detect a Lifshitz transition that separates two distinct superconducting regions. One emerges from the nematic phase with a small Fermi surface and strong electronic correlations, while the other one has a large Fermi surface and weak correlations that promotes nesting and stabilization of a magnetically ordered phase at high pressures. The absence of mass divergence at the nematic quantum phase transition suggests that the nematic fluctuations could be quenched by the strong coupling to the lattice or local strain effects. A direct consequence is the weakening of superconductivity at the nematic quantum phase transition in the absence of magnetically driven fluctuations.