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SignificanceSr2RuO4 is distinctive among unconventional superconductors, in that in addition to exhibiting evidence for strong correlations, it is stoichiometric and extremely clean. As a result, its electronic structure is unusually well characterized, rendering it an ideal platform for developing a deep understanding of the mechanism behind the emergence of the superconducting state from a Fermi liquid. Toward that end, an unambiguous determination of the pairing symmetry is an essential step. For more than 2 decades, the preponderance of evidence pointed to a triplet spin pairing state and only recently has this interpretation been challenged. By field-dependent NMR Knight shift measurements, we eliminate from further consideration all candidate purely odd-parity triplet pairing states. Unambiguous identification of the superconducting order parameter symmetry in Sr2RuO4 has remained elusive for more than a quarter century. While a chiral p-wave ground state analogue to superfluid 3He-A was ruled out only very recently, other proposed triplet-pairing scenarios are still viable. Establishing the condensate magnetic susceptibility reveals a sharp distinction between even-parity (singlet) and odd-parity (triplet) pairing since the superconducting condensate is magnetically polarizable only in the latter case. Here field-dependent 17O Knight shift measurements, being sensitive to the spin polarization, are compared to previously reported specific heat measurements for the purpose of distinguishing the condensate contribution from that due to quasiparticles. We conclude that the shift results can be accounted for entirely by the expected field-induced quasiparticle response. An upper bound for the condensate magnetic response of <10% of the normal state susceptibility is sufficient to exclude all purely odd-parity candidates.

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 emergence of superconductivity and correlated insulators in magic-angle twisted bilayer graphene (MATBG) has raised the intriguing possibility that its pairing mechanism is distinct from that of conventional superconductors 1 – 4 , as described by the Bardeen–Cooper–Schrieffer (BCS) theory. However, recent studies have shown that superconductivity persists even when Coulomb interactions are partially screened 5 , 6 . This suggests that pairing in MATBG might be conventional in nature and a consequence of the large density of states of its flat bands. Here we combine tunnelling and Andreev reflection spectroscopy with a scanning tunnelling microscope to observe several key experimental signatures of unconventional superconductivity in MATBG. We show that the tunnelling spectra below the transition temperature T c are inconsistent with those of a conventional s -wave superconductor, but rather resemble those of a nodal superconductor with an anisotropic pairing mechanism. We observe a large discrepancy between the tunnelling gap Δ T , which far exceeds the mean-field BCS ratio (with 2 Δ T / k B T c  ~ 25), and the gap Δ AR extracted from Andreev reflection spectroscopy (2 Δ AR / k B T c  ~ 6). The tunnelling gap persists even when superconductivity is suppressed, indicating its emergence from a pseudogap phase. Moreover, the pseudogap and superconductivity are both absent when MATBG is aligned with hexagonal boron nitride. These findings and other observations reported here provide a preponderance of evidence for a non-BCS mechanism for superconductivity in MATBG. A study combining tunnelling and Andreev reflection spectroscopy with a scanning tunnelling microscope provides evidence for unconventional superconductivity in magic-angle twisted bilayer graphene.

The behaviour of strongly correlated materials, and in particular unconventional superconductors, has been studied extensively for decades, but is still not well understood. This lack of theoretical understanding has motivated the development of experimental techniques for studying such behaviour, such as using ultracold atom lattices to simulate quantum materials. Here we report the realization of intrinsic unconventional superconductivity—which cannot be explained by weak electron–phonon interactions—in a two-dimensional superlattice created by stacking two sheets of graphene that are twisted relative to each other by a small angle. For twist angles of about 1.1°—the first ‘magic’ angle—the electronic band structure of this ‘twisted bilayer graphene’ exhibits flat bands near zero Fermi energy, resulting in correlated insulating states at half-filling. Upon electrostatic doping of the material away from these correlated insulating states, we observe tunable zero-resistance states with a critical temperature of up to 1.7 kelvin. The temperature–carrier-density phase diagram of twisted bilayer graphene is similar to that of copper oxides (or cuprates), and includes dome-shaped regions that correspond to superconductivity. Moreover, quantum oscillations in the longitudinal resistance of the material indicate the presence of small Fermi surfaces near the correlated insulating states, in analogy with underdoped cuprates. The relatively high superconducting critical temperature of twisted bilayer graphene, given such a small Fermi surface (which corresponds to a carrier density of about 10 11 per square centimetre), puts it among the superconductors with the strongest pairing strength between electrons. Twisted bilayer graphene is a precisely tunable, purely carbon-based, two-dimensional superconductor. It is therefore an ideal material for investigations of strongly correlated phenomena, which could lead to insights into the physics of high-critical-temperature superconductors and quantum spin liquids. A superlattice consisting of two graphene sheets twisted relative to each other by a specific amount exhibits superconductivity when doped electrostatically, with a relatively high critical temperature. Twisted graphene strengthens electronic interactions In 1957, John Bardeen, Leon Cooper, and John Robert Schrieffer came up with the first theory of superconductivity to describe how some materials can conduct electricity with no electrical resistance. However, there are many superconductive materials that cannot be described using this theory. Understanding the mechanism of unconventional superconductivity could help scientists engineer materials with higher transition temperatures. Pablo Jarillo-Herrero and colleagues now show that when two graphene sheets are twisted by a certain angle they exhibit unconventional superconductivity, with features similar to high-temperature superconducting cuprates. This system can easily be tuned through both the twist angle and electric fields, so could provide a new two-dimensional platform for understanding the origin of high-temperature superconductivity. Elsewhere in this issue, the same team reports that twisting graphene sheets in this manner also creates an insulating state that appears to be driven by strong electronic interactions, consistent with a Mott-like insulator phase.

Chiral superconductors are unconventional superconducting states that break time-reversal symmetry spontaneously and typically feature Cooper pairing at non-zero angular momentum. Such states may host Majorana fermions and provide an important platform for topological physics research and fault-tolerant quantum computing 1 , 2 , 3 , 4 , 5 , 6 – 7 . Despite intensive search and prolonged studies of several candidate systems 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 – 26 , chiral superconductivity has remained elusive so far. Here we report the discovery of robust unconventional superconductivity in rhombohedral tetralayer and pentalayer graphene without moiré superlattice effects. We observed two superconducting states in the gate-induced flat conduction bands with T c up to 300 mK and charge density n e down to 2.4 × 10 11  cm −2 in five devices. Spontaneous time-reversal-symmetry breaking (TRSB) owing to orbital motion of the electron is found and several observations indicate the chiral nature of these superconducting states, including: (1) in the superconducting state, R xx shows magnetic hysteresis in varying out-of-plane magnetic field B ⊥ —absent from all other superconductors; (2) the superconducting states are robust against in-plane magnetic field and are developed within a spin-polarized and valley-polarized quarter-metal (QM) phase; (3) the normal states show anomalous Hall signals at zero magnetic field and magnetic hysteresis. We also observed a critical B ⊥ of 1.4 T, higher than any graphene superconductivity, which indicates a strong-coupling superconductivity close to the Bardeen–Cooper–Schrieffer (BCS)–Bose–Einstein condensate (BEC) crossover 27 . Our observations establish a pure carbon material for the study of topological superconductivity, with the promise to explore Majorana modes and topological quantum computing. Observations indicating the chiral nature of superconducting states in five rhombohedral tetralayer and pentalayer graphene devices without moiré superlattice effects are reported, establishing a pure carbon material for the study of topological superconductivity.

One of the main developments in unconventional superconductivity in the past two decades has been the discovery that most unconventional superconductors form phase diagrams that also contain other strongly correlated states. Many systems of interest are therefore close to more than one instability, and tuning between the resultant ordered phases is the subject of intense research 1 . In recent years, uniaxial pressure applied using piezoelectric-based devices has been shown to be a particularly versatile new method of tuning 2 , 3 , leading to experiments that have advanced our understanding of the fascinating unconventional superconductor Sr 2 RuO 4 (refs.  4 – 9 ). Here we map out its phase diagram using high-precision measurements of the elastocaloric effect in what we believe to be the first such study including both the normal and the superconducting states. We observe a strong entropy quench on entering the superconducting state, in excellent agreement with a model calculation for pairing at the Van Hove point, and obtain a quantitative estimate of the entropy change associated with entry to a magnetic state that is observed in proximity to the superconductivity. The phase diagram is intriguing both for its similarity to those seen in other families of unconventional superconductors and for extra features unique, so far, to Sr 2 RuO 4 . The phase diagram of the unconventional superconductor Sr 2 RuO 4 in both normal and superconducting states is mapped out using high-precision measurements of the elastocaloric effect, showing similarities to other unconventional superconductors as well as unique features.

The kagome lattice 1 , which is the most prominent structural motif in quantum physics, benefits from inherent non-trivial geometry so that it can host diverse quantum phases, ranging from spin-liquid phases, to topological matter, to intertwined orders 2 – 8 and, most rarely, to unconventional superconductivity 6 , 9 . Recently, charge sensitive probes have indicated that the kagome superconductors A V 3 Sb 5 ( A = K, Rb, Cs) 9 – 11 exhibit unconventional chiral charge order 12 – 19 , which is analogous to the long-sought-after quantum order in the Haldane model 20 or Varma model 21 . However, direct evidence for the time-reversal symmetry breaking of the charge order remains elusive. Here we use muon spin relaxation to probe the kagome charge order and superconductivity in KV 3 Sb 5 . We observe a noticeable enhancement of the internal field width sensed by the muon ensemble, which takes place just below the charge ordering temperature and persists into the superconducting state. Notably, the muon spin relaxation rate below the charge ordering temperature is substantially enhanced by applying an external magnetic field. We further show the multigap nature of superconductivity in KV 3 Sb 5 and that the T c / λ a b − 2 ratio (where T c is the superconducting transition temperature and λ ab is the magnetic penetration depth in the kagome plane) is comparable to those of unconventional high-temperature superconductors. Our results point to time-reversal symmetry-breaking charge order intertwining with unconventional superconductivity in the correlated kagome lattice. An investigation of muon spin relaxation shows time-reversal symmetry-breaking charge order, intertwined with correlated superconductivity, due to orbital currents in the kagome superconductor KV 3 Sb 5 .

The recent discovery of superconductivity in oxygen-reduced monovalent nickelates has raised a new platform for the study of unconventional superconductivity, with similarities to and differences from the cuprate high-temperature superconductors. In this paper, we investigate the family of infinite-layer nickelatesRNiO2with rare-earthRspanning across the lanthanide series, introducing a new and nontrivial “knob” with which to tune nickelate superconductivity. When traversing from La to Lu, the out-of-plane lattice constant decreases dramatically with an accompanying increase of Nidx2−y2bandwidth; however, surprisingly, the role of oxygen charge transfer diminishes. In contrast, the magnetic exchange grows across the lanthanides, which may be favorable to superconductivity. Moreover, compensation effects from the itinerant5delectrons present a closer analogy to Kondo lattices, indicating a stronger interplay between charge transfer, bandwidth renormalization, compensation, and magnetic exchange. We also obtain the microscopic Hamiltonian using the Wannier downfolding technique, which will provide the starting point for further many-body theoretical studies.

Emergent electronic phenomena in iron-based superconductors have been at the forefront of condensed matter physics for more than a decade. Much has been learned about the origins and intertwined roles of ordered phases, including nematicity, magnetism, and superconductivity, in this fascinating class of materials. In recent years, focus has been centered on the peculiar and highly unusual properties of FeSe and its close cousins. This family of materials has attracted considerable attention due to the discovery of unexpected superconducting gap structures, a wide range of superconducting critical temperatures, and evidence for nontrivial band topology, including associated spin-helical surface states and vortex-induced Majorana bound states. Here, we review superconductivity in iron chalcogenide superconductors, including bulk FeSe, doped bulk FeSe, FeTe1−xSex, intercalated FeSe materials, and monolayer FeSe and FeTe1−xSex on SrTiO3. We focus on the superconducting properties, including a survey of the relevant experimental studies, and a discussion of the different proposed theoretical pairing scenarios. In the last part of the paper, we review the growing recent evidence for nontrivial topological effects in FeSe-related materials, focusing again on interesting implications for superconductivity.

We study electronic ordering instabilities of twisted bilayer graphene around the filling ofn=2electrons per supercell, where correlated insulator state and superconductivity have been recently observed. Motivated by the Fermi surface nesting and the proximity to Van Hove singularity, we introduce a hot-spot model to study the effect of various electron interactions systematically. Using the renormalization group method, we find thatdorp-wave superconductivity and charge or spin density wave emerge as the two types of leading instabilities driven by Coulomb repulsion. The density-wave state has a gapped energy spectrum aroundn=2and yields a single doubly degenerate pocket upon doping ton>2. The intertwinement of density wave and superconductivity and the quasiparticle spectrum in the density-wave state are consistent with experimental observations.