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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.

A key actor in the conventional theory of superconductivity is the induced interaction between electrons mediated by the exchange of virtual collective fluctuations (phonons in the case of conventional s-wave superconductors). Other collective modes that can play the same role, especially spin fluctuations, have been widely discussed in the context of high-temperature and heavy Fermion superconductors. The strength of such collective fluctuations is measured by the associated susceptibility. Here we use differential elastoresistance measurements from five optimally doped iron-based superconductors to show that divergent nematic susceptibility appears to be a generic feature in the optimal doping regime of these materials. This observation motivates consideration of the effects of nematic fluctuations on the superconducting pairing interaction in this family of compounds and possibly beyond.

Within the Landau paradigm of continuous phase transitions, ordered states of matter are characterized by a broken symmetry. Although the broken symmetry is usually evident, determining the driving force behind the phase transition can be complicated by coupling between distinct order parameters. We show how measurement of the divergent nematic susceptibility of the iron pnictide superconductor Ba(Fe 1−x Co x ) 2 As 2 distinguishes an electronic nematic phase transition from a simple ferroelastic distortion. These measurements also indicate an electronic nematic quantum phase transition near the composition with optimal superconducting transition temperature.

Revealing the presence of magnetic octupole order and associated octupole fluctuations in solids is a highly challenging task due to the lack of simple external fields that can couple to magnetic octupoles. Here, we demonstrate a methodology for probing the magnetic octupole susceptibility of a candidate material, PrV 2 Al 20 , using a product of magnetic field H i and shear strain ϵ j k as a composite effective field, while employing an adiabatic elastocaloric effect to probe the response. We observe Curie-Weiss behavior in the obtained octupolar susceptibility down to approximately 3 K. Although octupole order does not appear to be the leading multipolar channel in PrV 2 Al 20 , our results nevertheless reveal the presence of strong magnetic octupole fluctuations and hence demonstrate that octupole order is at least a competing state. More broadly, our results highlight how anisotropic strain can be combined with magnetic fields to probe elusive ‘hidden’ electronic orders. Magnetic dipoles are the lowest order term in a multipolar expansion. The next allowed in centrosymmetric materials is a magnetic octupole, but this is notoriously difficult to probe experimentally, due to a lack of direct coupling to external fields. Here, Ye et al demonstrate a method to overcome this in PrV 2 Al 20 .”

High-temperature superconductivity often emerges in the proximity of a symmetry-breaking ground state. For superconducting iron arsenides, in addition to the antiferromagnetic ground state, a small structural distortion breaks the crystal's C₄ rotational symmetry in the underdoped part of the phase diagram. We reveal that the representative iron arsenide Ba(Fe₁₋xCox)₂As₂ develops a large electronic anisotropy at this transition via measurements of the in-plane resistivity of detwinned single crystals, with the resistivity along the shorter b axis ρb being greater than ρa. The anisotropy reaches a maximum value of approximately 2 for compositions in the neighborhood of the beginning of the superconducting dome. For temperatures well above the structural transition, uniaxial stress induces a resistivity anisotropy, indicating a substantial nematic susceptibility.

For an ideal topological insulator, the metallic surface states should be easy to measure using transport techniques; however, the bulk is not completely insulating. Improving the ‘leaky’ bulk state proves crucial for measuring the surface Dirac fermions, including correlation effects. The topological insulator is a unique state of matter that possesses a metallic surface state of massless particles known as Dirac fermions, which have coupled spin and momentum quantum numbers. Owing to the preservation of time-reversal symmetry, this coupling protects the wavefunctions against disorder 1 , 2 , 3 . The experimental realization of this state of matter in Bi 2 Se 3 and Bi 2 Te 3 has sparked considerable interest owing both to their potential use in spintronic devices and in the investigation of the fundamental nature of topologically non-trivial quantum matter. However, the conductivity of these compounds tends to be dominated by the bulk of the material because of chemical imperfection, making the transport properties of the surface nearly impossible to measure. We have systematically reduced the number of bulk carriers in Bi 2 Se 3 to the point where a magnetic field can collapse them to their lowest Landau level. Beyond this field, known as the three-dimensional (3D) ‘quantum limit’, the signature of the 2D surface state can be seen. At still higher fields, we reach the 2D quantum limit of the surface Dirac fermions. In this limit we observe an altered phase of the oscillations, which is related to the peculiar nature of the Landau quantization of topological insulators at high field. Furthermore, we observe quantum oscillations corresponding to fractions of the Landau integers, suggesting that correlation effects can be observed in this new state of quantum matter.

The elastocaloric effect (ECE) relates changes in entropy to changes in strain experienced by a material. As such, ECE measurements can provide valuable information about the entropy landscape proximate to strain-tuned phase transitions. For ordered states that break only point symmetries, bilinear coupling of the order parameter with strain implies that the ECE can also provide a window on fluctuations above the critical temperature and hence, in principle, can also provide a thermodynamic measure of the associated susceptibility. To demonstrate this, we use the ECE to sensitively reveal the presence of nematic fluctuations in the archetypal Fe-based superconductor Ba(Fe1–xCoₓ)₂As₂. By performing these measurements simultaneously with elastoresistivity in a multimodal fashion, we are able to make a direct and unambiguous comparison of these closely related thermodynamic and transport properties, both of which are sensitive to nematic fluctuations. As a result, we have uncovered an unanticipated doping dependence of the nemato-elastic coupling and of the magnitude of the scattering of low-energy quasi-particles by nematic fluctuations—while the former weakens, the latter increases dramatically with increasing doping.

The speed with which symmetry breaking transitions occur in the solid state makes them difficult to study in the time domain. State-of-the-art pump–probe measurements of the dynamics of charge-density waves in terbium telluride enable the evolution of the symmetry breaking charge-order transition of this system to be studied with unprecedented temporal resolution. The study of the temporal evolution of systems undergoing symmetry breaking phase transitions—whether it is in condensed-matter physics, cosmology or finance 1 , 2 , 3 , 4 , 5 , 6 —is difficult because they are hard to repeat, or they occur very rapidly. Here we report a high-time-resolution study of the evolution of both bosonic and fermionic excitations through an electronic charge-ordering symmetry breaking phase transition. Periodically quenching our system with femtosecond optical pulses, we subsequently detect hitherto-unrecorded coherent aperiodic undulations of the order parameter, critical slowing down of the collective mode and evolution of the particle–hole gap as the system evolves through the transition. Modelling on the basis of Ginzburg–Landau theory is used to reproduce the observations without free parameters. Of particular interest is the observation of spectrotemporal distortions arising from spontaneous annihilation of topological defects, analogous to those discussed by the Kibble–Zurek cosmological model 2 , 3 .

Nematicity, defined as broken rotational symmetry, has recently been observed in competing phases proximate to the superconducting phase in the cuprate high-temperature superconductors. Similarly, the new iron-based high-temperature superconductors exhibit a tetragonal-to-orthorhombic structural transition (i.e., a broken C₄ symmetry) that either precedes or is coincident with a collinear spin density wave (SDW) transition in undoped parent compounds, and superconductivity arises when both transitions are suppressed via doping. Evidence for strong in-plane anisotropy in the SDW state in this family of compounds has been reported by neutron scattering, scanning tunneling microscopy, and transport measurements. Here, we present an angle-resolved photoemission spectroscopy study of detwinned single crystals of a representative family of electron-doped iron-arsenide superconductors, Ba(Fe1-xCox)₂As₂ in the underdoped region. The crystals were detwinned via application of in-plane uniaxial stress, enabling measurements of single domain electronic structure in the orthorhombic state. At low temperatures, our results clearly demonstrate an in-plane electronic anisotropy characterized by a large energy splitting of two orthogonal bands with dominant dxz and dyz character, which is consistent with anisotropy observed by other probes. For compositions x > 0, for which the structural transition (Ts) precedes the magnetic transition (TSDW), an anisotropic splitting is observed to develop above TSDW, indicating that it is specifically associated with TS. For unstressed crystals, the band splitting is observed close to Ts. whereas for stressed crystals, the splitting is observed to considerably higher temperatures, revealing the presence of a surprisingly large in-plane nematic susceptibility in the electronic structure.

Topological insulators exhibit a bulk energy gap and spin-polarized surface states that lead to unique electronic properties 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , with potential applications in spintronics and quantum information processing. However, transport measurements have typically been dominated by residual bulk charge carriers originating from crystal defects or environmental doping 10 , 11 , 12 , and these mask the contribution of surface carriers to charge transport in these materials. Controlling bulk carriers in current topological insulator materials, such as the binary sesquichalcogenides Bi 2 Te 3 , Sb 2 Te 3 and Bi 2 Se 3 , has been explored extensively by means of material doping 8 , 9 , 11 and electrical gating 13 , 14 , 15 , 16 , but limited progress has been made to achieve nanostructures with low bulk conductivity for electronic device applications. Here we demonstrate that the ternary sesquichalcogenide (Bi x Sb 1– x ) 2 Te 3 is a tunable topological insulator system. By tuning the ratio of bismuth to antimony, we are able to reduce the bulk carrier density by over two orders of magnitude, while maintaining the topological insulator properties. As a result, we observe a clear ambipolar gating effect in (Bi x Sb 1– x ) 2 Te 3 nanoplate field-effect transistor devices, similar to that observed in graphene field-effect transistor devices 17 . The manipulation of carrier type and density in topological insulator nanostructures demonstrated here paves the way for the implementation of topological insulators in nanoelectronics and spintronics. The bulk conductivity of a topological insulator composed of Bi, Sb and Te can be reduced by orders of magnitude by tuning the ratio of Bi to Sb, allowing surface states to dominate conduction.