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Based on the random phase approximation calculation in two-orbital honeycomb lattice model, we investigate the pairing symmetry of Ni-based transition-metal trichalcogenides by electron doping access to type-II van Hove singularities (vHs). We find that chiral even-parity d + i d -wave ( E g ) state is suppressed by odd-parity p + i p -wave ( E u ) state when electron doping approaches the type-II vHs. The type-II vHs peak in density of states (DOS) enables to strengthen the ferromagnetic fluctuation, which is responsible for triplet pairing. The competition between antiferromagnetic and ferromagnetic fluctuation results in pairing phase transition from singlet to triplet pairing. The Ni-based transition-metal trichalcogenides provide a promising platform to unconventional superconductor emerging from electronic DOS.

Although high-transition-temperature (high- T c ) superconductivity in cuprates has been known for more than three decades, the underlying mechanism remains unknown 1 – 4 . Cuprates are the only unconventional superconductors that exhibit bulk superconductivity with T c above the liquid-nitrogen boiling temperature of 77 K. Here we observe that high-pressure resistance and mutual inductive magnetic susceptibility measurements showed signatures of superconductivity in single crystals of La 3 Ni 2 O 7 with maximum T c of 80 K at pressures between 14.0 GPa and 43.5 GPa. The superconducting phase under high pressure has an orthorhombic structure of Fmmm space group with the 3 d x 2 − y 2 and 3 d z 2 orbitals of Ni cations strongly mixing with oxygen 2 p orbitals. Our density functional theory calculations indicate that the superconductivity emerges coincidently with the metallization of the σ-bonding bands under the Fermi level, consisting of the 3 d z 2 orbitals with the apical oxygen ions connecting the Ni–O bilayers. Thus, our discoveries provide not only important clues for the high- T c superconductivity in this Ruddlesden–Popper double-layered perovskite nickelates but also a previously unknown family of compounds to investigate the high- T c superconductivity mechanism. Signatures of superconductivity in single crystals of La 3 Ni 2 O 7 were observed at a maximum transition temperature of 80  K at pressures between 14.0  GPa and 43.5  GPa.

Electronic nematicity, in which rotational symmetry is spontaneously broken by electronic degrees of freedom, has been demonstrated as a ubiquitous phenomenon in correlated quantum fluids including high-temperature superconductors and quantum Hall systems 1 , 2 . Notably, the electronic nematicity in high-temperature superconductors exhibits an intriguing entanglement with superconductivity, generating complicated superconducting pairing and intertwined electronic orders. Recently, an unusual competition between superconductivity and a charge-density-wave (CDW) order has been found in the A V 3 Sb 5 ( A  = K, Rb, Cs) family with two-dimensional vanadium kagome nets 3 – 8 . Whether these phenomena involve electronic nematicity is still unknown. Here we report evidence for the existence of electronic nematicity in CsV 3 Sb 5 , using a combination of elastoresistance measurements, nuclear magnetic resonance (NMR) and scanning tunnelling microscopy/spectroscopy (STM/S). The temperature-dependent elastoresistance coefficient ( m 11 minus m 12 ) and NMR spectra demonstrate that, besides a C 2 structural distortion of the 2 a 0  × 2 a 0 supercell owing to out-of-plane modulation, considerable nematic fluctuations emerge immediately below the CDW transition (approximately 94 kelvin) and finally a nematic transition occurs below about 35 kelvin. The STM experiment directly visualizes the C 2 -structure-pinned long-range nematic order below the nematic transition temperature, suggesting a novel nematicity described by a three-state Potts model. Our findings indicate an intrinsic electronic nematicity in the normal state of CsV 3 Sb 5 , which sets a new paradigm for revealing the role of electronic nematicity on pairing mechanism in unconventional superconductors. Charge-density-wave-driven electronic nematicity that occurs well below the charge-density-wave transition temperature is reported in the kagome superconductor CsV 3 Sb 5 .

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 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.

The discovery of superconducting and insulating states in magic-angle twisted bilayer graphene (MATBG) 1 , 2 has ignited considerable interest in understanding the nature of electronic interactions in this chemically pristine material. The transport properties of MATBG as a function of doping are similar to those of high-transition-temperature copper oxides and other unconventional superconductors 1 – 3 , which suggests that MATBG may be a highly interacting system. However, to our knowledge, there is no direct experimental evidence of strong many-body correlations in MATBG. Here we present high-resolution spectroscopic measurements, obtained using a scanning tunnelling microscope, that provide such evidence as a function of carrier density. MATBG displays unusual spectroscopic characteristics that can be attributed to electron–electron interactions over a wide range of doping levels, including those at which superconductivity emerges in this system. We show that our measurements cannot be explained with a mean-field approach for modelling electron–electron interactions in MATBG. The breakdown of a mean-field approach when applied to other correlated superconductors, such as copper oxides, has long inspired the study of the highly correlated Hubbard model 3 . We show that a phenomenological extended-Hubbard-model cluster calculation, which is motivated by the nearly localized nature of the relevant electronic states of MATBG, produces spectroscopic features that are similar to those that we observed experimentally. Our findings demonstrate the critical role of many-body correlations in understanding the properties of MATBG. Scanning tunnelling spectroscopy and extended-Hubbard-model cluster calculations reveal that magic-angle twisted bilayer graphene is a strongly correlated electron system, similar to other unconventional superconductors.

Recent experimental observations have showed some signatures of superconductivity close to 80 K in La 3 Ni 2 O 7 under pressure and have raised the hope of achieving high-temperature superconductivity in bulk nickelates. However, a zero-resistance state—a key characteristic of a superconductor—was not observed. Here we show that the zero-resistance state does exist in single crystals of La 3 Ni 2 O 7− δ using a liquid pressure medium at up to 30 GPa. We also find that the system remains metallic under applied pressures, suggesting the absence of a metal–insulator transition proximate to the superconductivity. Moreover, analysis of the normal state T -linear resistance reveals a link between this strange-metal behaviour and superconductivity. The association between strange-metal behaviour and high-temperature superconductivity is very much in line with other classes of unconventional superconductors, including the cuprates and Fe-based superconductors. Further investigations exploring the interplay of strange-metal behaviour and superconductivity, as well as possible competing electronic or structural phases, are essential to understand the mechanism of superconductivity in this system. Some features resembling superconductivity at high temperature have been seen under pressure in La 3 Ni 2 O 7 , but a transition to a zero-resistance state has not been observed. Now transport studies demonstrate this transition, along with strange metallicity.

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.

Marked evolution of properties with minute changes in the doping level is a hallmark of the complex chemistry that governs copper oxide superconductivity as manifested in the celebrated superconducting domes and quantum criticality taking place at precise compositions 1 – 4 . The strange-metal state, in which the resistivity varies linearly with temperature, has emerged as a central feature in the normal state of copper oxide superconductors 5 – 9 . The ubiquity of this behaviour signals an intimate link between the scattering mechanism and superconductivity 10 – 12 . However, a clear quantitative picture of the correlation has been lacking. Here we report the observation of precise quantitative scaling laws among the superconducting transition temperature ( T c ), the linear-in- T scattering coefficient ( A 1 ) and the doping level ( x ) in electron-doped copper oxide La 2– x Ce x CuO 4 (LCCO). High-resolution characterization of epitaxial composition-spread films, which encompass the entire overdoped range of LCCO, has enabled us to systematically map its structural and transport properties with unprecedented accuracy and with increments of Δ x  = 0.0015. We have uncovered the relations T c ~ ( x c – x ) 0.5 ~ ( A 1 □ ) 0.5 , where x c is the critical doping in which superconductivity disappears and A 1 □ is the coefficient of the linear resistivity per CuO 2 plane. The striking similarity of the T c versus A 1 □ relation among copper oxides, iron-based and organic superconductors may be an indication of a common mechanism of the strange-metal behaviour and unconventional superconductivity in these systems. Precise quantitative scaling laws are observed between the normalized T -linear coefficient and T c among copper oxides, pnictides and a class of organic superconductors, suggesting a common underlying physics at work in these unconventional superconductors.

We build symmetry-adapted maximally localized Wannier states and construct the low-energy tight-binding model for the four narrow bands of twisted bilayer graphene. We do so when the twist angle is commensurate near the “magic” value and the narrow bands are separated from the rest of the bands by energy gaps. On each layer and sublattice, every Wannier state has three peaks near the triangular moiré lattice sites. However, each Wannier state is localized and centered around a site of the honeycomb lattice that is dual to the triangular moiré lattice. The space group and the time-reversal symmetries are realized locally. The corresponding tight-binding model provides a starting point for studying the correlated many-body phases.