Evolution of superconductivity in twisted graphene multilayers.

The group of moiré graphene superconductors keeps growing, and by now it contains twisted graphene multilayers as well as untwisted stacks. We analyze here the contribution of long-range charge fluctuations in the superconductivity of twisted double bilayers and helical trilayers, and compare the results to twisted bilayer graphene. A diagrammatic approach which depends on a few, well-known parameters is used. We find that the critical temperature and the order parameter differ significantly between twisted double bilayers and helical trilayers on one hand, and twisted bilayer graphene on the other. This trend, consistent with experiments, can be associated with the role played by moiré Umklapp processes in the different systems.

Predicted hot superconductivity in LaSc2H24 under pressure.

The recent theory-driven discovery of a class of clathrate hydrides (e.g., CaH6, YH6, YH9, and LaH10) with superconducting critical temperatures (Tc) well above 200 K has opened the prospects for "hot" superconductivity above room temperature under pressure. Recent efforts focus on the search for superconductors among ternary hydrides that accommodate more diverse material types and configurations compared to binary hydrides. Through extensive computational searches, we report the prediction of a unique class of thermodynamically stable clathrate hydrides structures consisting of two previously unreported H24 and H30 hydrogen clathrate cages at megabar pressures. Among these phases, LaSc2H24 shows potential hot superconductivity at the thermodynamically stable pressure range of 167 to 300 GPa, with calculated Tcs up to 331 K at 250 GPa and 316 K at 167 GPa when the important effects of anharmonicity are included. The very high critical temperatures are attributed to an unusually large hydrogen-derived density of states at the Fermi level arising from the newly reported peculiar H30 as well as H24 cages in the structure. Our predicted introduction of Sc in the La-H system is expected to facilitate future design and realization of hot superconductors in ternary clathrate superhydrides.

Chemical bonding dictates drastic critical temperature difference in two seemingly identical superconductors.

Though YB6 and LaB6 share the same crystal structure, atomic valence electron configuration, and phonon modes, they exhibit drastically different phonon-mediated superconductivity. YB6 superconducts below 8.4 K, giving it the second-highest critical temperature of known borides, second only to MgB2. LaB6 does not superconduct until near-absolute zero temperatures (below 0.45 K), however. Though previous studies have quantified the canonical superconductivity descriptors of YB6's greater Fermi-level (Ef) density of states and higher electron-phonon coupling (EPC), the root of this difference has not been assessed with full detail of the electronic structure. Through chemical bonding, we determine low-lying, unoccupied 4f atomic orbitals in lanthanum to be the key difference between these superconductors. These orbitals, which are not accessible in YB6, hybridize with π B-B bonds and bring this π-system lower in energy than the σ B-B bonds otherwise at Ef. This inversion of bands is crucial: the optical phonon modes we show responsible for superconductivity cause the σ-orbitals of YB6 to change drastically in overlap, but couple weakly to the π-orbitals of LaB6. These phonons in YB6 even access a crossing of electronic states, indicating strong EPC. No such crossing in LaB6 is observed. Finally, a supercell (the M k-point) is shown to undergo Peierls-like effects in YB6, introducing additional EPC from both softened acoustic phonons and the same electron-coupled optical modes as in the unit cell. Overall, we find that LaB6 and YB6 have fundamentally different mechanisms of superconductivity, despite their otherwise near-identity.

Enhanced triplet superconductivity in next-generation ultraclean UTe2.

The unconventional superconductor UTe[Formula: see text] exhibits numerous signatures of spin-triplet superconductivity-a rare state of matter which could enable quantum computation protected against decoherence. UTe[Formula: see text] possesses a complex phase landscape comprising two magnetic field-induced superconducting phases, a metamagnetic transition to a field-polarized state, along with pair- and charge-density wave orders. However, contradictory reports between studies performed on UTe[Formula: see text] specimens of varying quality have severely impeded theoretical efforts to understand the microscopic origins of the exotic superconductivity. Here, we report a comprehensive suite of high magnetic field measurements on a generation of pristine quality UTe[Formula: see text] crystals. Our experiments reveal a significantly revised high magnetic field superconducting phase diagram in the ultraclean limit, showing a pronounced sensitivity of field-induced superconductivity to the presence of crystalline disorder. We employ a Ginzburg-Landau model that excellently captures this acute dependence on sample quality. Our results suggest that in close proximity to a field-induced metamagnetic transition the enhanced role of magnetic fluctuations-that are strongly suppressed by disorder-is likely responsible for tuning UTe[Formula: see text] between two distinct spin-triplet superconducting phases.

Collective neural network behavior in a dynamically driven disordered system of superconducting loops.

Collective properties of complex systems composed of many interacting components such as neurons in our brain can be modeled by artificial networks based on disordered systems. We show that a disordered neural network of superconducting loops with Josephson junctions can exhibit computational properties like categorization and associative memory in the time evolution of its state in response to information from external excitations. Superconducting loops can trap multiples of fluxons in many discrete memory configurations defined by the local free energy minima in the configuration space of all possible states. A memory state can be updated by exciting the Josephson junctions to fire or allow the movement of fluxons through the network as the current through them surpasses their critical current thresholds. Simulations performed with a lumped element circuit model of a 4-loop network show that information written through excitations is translated into stable states of trapped flux and their time evolution. Experimental implementation on a high-Tc superconductor YBCO-based 4-loop network shows dynamically stable flux flow in each pathway characterized by the correlations between junction firing statistics. Neural network behavior is observed as energy barriers separating state categories in simulations in response to multiple excitations, and experimentally as junction responses characterizing different flux flow patterns in the network. The state categories that produce these patterns have different temporal stabilities relative to each other and the excitations. This provides strong evidence for time-dependent (short-to-long-term) memories, that are dependent on the geometrical and junction parameters of the loops, as described with a network model.

Designing the stripe-ordered cuprate phase diagram through uniaxial-stress.

The ability to efficiently control charge and spin in the cuprate high-temperature superconductors is crucial for fundamental research and underpins technological development. Here, we explore the tunability of magnetism, superconductivity, and crystal structure in the stripe phase of the cuprate La[Formula: see text]Ba[Formula: see text]CuO[Formula: see text], with [Formula: see text] = 0.115 and 0.135, by employing temperature-dependent (down to 400 mK) muon-spin rotation and AC susceptibility, as well as X-ray scattering experiments under compressive uniaxial stress in the CuO[Formula: see text] plane. A sixfold increase of the three-dimensional (3D) superconducting critical temperature [Formula: see text] and a full recovery of the 3D phase coherence is observed in both samples with the application of extremely low uniaxial stress of [Formula: see text]0.1 GPa. This finding demonstrates the removal of the well-known 1/8-anomaly of cuprates by uniaxial stress. On the other hand, the spin-stripe order temperature as well as the magnetic fraction at 400 mK show only a modest decrease under stress. Moreover, the onset temperatures of 3D superconductivity and spin-stripe order are very similar in the large stress regime. However, strain produces an inhomogeneous suppression of the spin-stripe order at elevated temperatures. Namely, a substantial decrease of the magnetic volume fraction and a full suppression of the low-temperature tetragonal structure is found under stress, which is a necessary condition for the development of the 3D superconducting phase with optimal [Formula: see text]. Our results evidence a remarkable cooperation between the long-range static spin-stripe order and the underlying crystalline order with the three-dimensional fully coherent superconductivity. Overall, these results suggest that the stripe- and the SC order may have a common physical mechanism.

How pressure enhances the critical temperature of superconductivity in YBa2Cu3O6+y.

High-temperature superconducting cuprates respond to doping with a dome-like dependence of their critical temperature (Tc). But the family-specific maximum Tc can be surpassed by application of pressure, a compelling observation known for decades. We investigate the phenomenon with high-pressure anvil cell NMR and measure the charge content at planar Cu and O, and with it the doping of the ubiquitous CuO2 plane with atomic-scale resolution. We find that pressure increases the overall hole doping, as widely assumed, but when it enhances Tc above what can be achieved by doping, pressure leads to a hole redistribution favoring planar O. This is similar to the observation that the family-specific maximum Tc is higher for materials where the hole content at planar O is higher at the expense of that at planar Cu. The latter reflects dependence of the maximum Tc on the Cu-O bond covalence and the charge-transfer gap. The results presented here indicate that the pressure-induced enhancement of the maximum Tc points to the same mechanism.

Diamagnetic response and phase stiffness for interacting isolated narrow bands.

Superconductivity is a macroscopic manifestation of a quantum phenomenon where pairs of electrons delocalize and develop phase coherence over a long distance. A long-standing quest has been to address the underlying microscopic mechanisms that fundamentally limit the superconducting transition temperature, Tc. A platform which serves as an ideal playground for realizing "high"-temperature superconductors are materials where the electrons' kinetic energy is quenched and interactions provide the only energy scale in the problem. However, when the noninteracting bandwidth for a set of isolated bands is small compared to the interactions, the problem is inherently nonperturbative. In two spatial dimensions, Tc is controlled by superconducting phase stiffness. Here, we present a theoretical framework for computing the electromagnetic response for generic model Hamiltonians, which controls the maximum possible superconducting phase stiffness and thereby Tc, without resorting to any mean-field approximation. Our explicit computations demonstrate that the contribution to the phase stiffness arises from i) "integrating out" the remote bands that couple to the microscopic current operator and ii) the density-density interactions projected on to the isolated narrow bands. Our framework can be used to obtain an upper bound on the phase stiffness and relatedly Tc for a range of physically inspired models involving both topological and nontopological narrow bands with density-density interactions. We discuss a number of salient aspects of this formalism by applying it to a specific model of interacting flat bands and compare the upper bound against the known Tc from independent numerically exact computations.

Evidence for an emergent anomalous metallic state in compressed titanium.

The anomalous metallic state (AMS) emerging from a quantum superconductor-to-metal transition is a subject of great current interest since this exotic quantum state exhibits unconventional transport properties that challenge the core physics principles of Fermi liquid theory. As the AMS concept is historically derived from disordered two-dimensional (2D) systems, related studies have predominately concentrated on 2D materials. The AMS behaviors in three-dimensional (3D) systems have been rarely reported to date, which raises intriguing questions on the fundamental nature of pertinent physics. Here, we report experimental evidence for a 3D AMS in highly compressed titanium metal that exhibits superconductivity with a critical temperature (Tc) reaching near-record 25.1 K among elemental superconductors, offering a favorable material template for exploring 3D AMS. At sufficiently strong magnetic fields, unusual transport behaviors set in over a wide pressure range, showcasing AMS hallmarks of a low-temperature saturation resistance below the Drude value and giant positive magnetoresistance. These findings reveal a 3D AMS in simple elemental systems and, more importantly, provide a fresh platform for probing the decades-long enigmatic underlying physics.

Signatures of Cooper pair dynamics and quantum-critical superconductivity in tunable carrier bands.

Different superconducting pairing mechanisms are markedly distinct in the underlying Cooper pair kinematics. Quantum-critical soft modes drive pairing interactions in which the pair scattering processes are highly collinear and can be classified into two categories: forward scattering and backscattering. Conversely, in conventional phonon mechanisms, Cooper pair scattering is of a generic noncollinear character. In this study, we present a method to discern the kinematic type by observing the evolution of superconductivity while adjusting the Fermi surface geometry. To demonstrate our approach, we utilize the recently reported phase diagrams of untwisted graphene multilayers. Our analysis connects the emergence of superconductivity at "ghost crossings" of Fermi surfaces in distinct valleys to the pair kinematics of a backscattering type. Together with the observed nonmonotonic behavior of superconductivity near its onset (sharp rise followed by a drop), it lends strong support to a particular quantum-critical superconductivity scenario in which pairing is driven by intervalley coherence fluctuations. These findings offer direct insights into the genesis of pairing in these systems, providing compelling evidence for the electron-electron interactions driving superconductivity. More broadly, our work highlights the potential of tuning bands via ghost crossings as a promising means of boosting superconductivity.

Ubiquitous coexisting electron-mode couplings in high-temperature cuprate superconductors.

In conventional superconductors, electron-phonon coupling plays a dominant role in generating superconductivity. In high-temperature cuprate superconductors, the existence of electron coupling with phonons and other boson modes and its role in producing high-temperature superconductivity remain unclear. The evidence of electron-boson coupling mainly comes from angle-resolved photoemission (ARPES) observations of [Formula: see text]70-meV nodal dispersion kink and [Formula: see text]40-meV antinodal kink. However, the reported results are sporadic and the nature of the involved bosons is still under debate. Here we report findings of ubiquitous two coexisting electron-mode couplings in cuprate superconductors. By taking ultrahigh-resolution laser-based ARPES measurements, we found that the electrons are coupled simultaneously with two sharp modes at [Formula: see text]70meV and [Formula: see text]40meV in different superconductors with different dopings, over the entire momentum space and at different temperatures above and below the superconducting transition temperature. These observations favor phonons as the origin of the modes coupled with electrons and the observed electron-mode couplings are unusual because the associated energy scales do not exhibit an obvious energy shift across the superconducting transition. We further find that the well-known "peak-dip-hump" structure, which has long been considered a hallmark of superconductivity, is also omnipresent and consists of "peak-double dip-double hump" finer structures that originate from electron coupling with two sharp modes. These results provide a unified picture for the [Formula: see text]70-meV and [Formula: see text]40-meV energy scales and their evolutions with momentum, doping and temperature. They provide key information to understand the origin of these energy scales and their role in generating anomalous normal state and high-temperature superconductivity.

A model of d-wave superconductivity, antiferromagnetism, and charge order on the square lattice.

We describe the confining instabilities of a proposed quantum spin liquid underlying the pseudogap metal state of the hole-doped cuprates. The spin liquid can be described by a SU(2) gauge theory of Nf = 2 massless Dirac fermions carrying fundamental gauge charges-this is the low-energy theory of a mean-field state of fermionic spinons moving on the square lattice with π-flux per plaquette in the ℤ2 center of SU(2). This theory has an emergent SO(5)f global symmetry and is presumed to confine at low energies to the Néel state. At nonzero doping (or smaller Hubbard repulsion U at half-filling), we argue that confinement occurs via the Higgs condensation of bosonic chargons carrying fundamental SU(2) gauge charges also moving in π ℤ2-flux. At half-filling, the low-energy theory of the Higgs sector has Nb = 2 relativistic bosons with a possible emergent SO(5)b global symmetry describing rotations between a d-wave superconductor, period-2 charge stripes, and the time-reversal breaking "d-density wave" state. We propose a conformal SU(2) gauge theory with Nf = 2 fundamental fermions, Nb = 2 fundamental bosons, and a SO(5)f×SO(5)b global symmetry, which describes a deconfined quantum critical point between a confining state which breaks SO(5)f and a confining state which breaks SO(5)b. The pattern of symmetry breaking within both SO(5)s is determined by terms likely irrelevant at the critical point, which can be chosen to obtain a transition between Néel order and d-wave superconductivity. A similar theory applies at nonzero doping and large U, with longer-range couplings of the chargons leading to charge order with longer periods.

Two superconducting states with broken time-reversal symmetry in FeSe1-xSx.

Iron-chalcogenide superconductors FeSe1-xSx possess unique electronic properties such as nonmagnetic nematic order and its quantum critical point. The nature of superconductivity with such nematicity is important for understanding the mechanism of unconventional superconductivity. A recent theory suggested the possible emergence of a fundamentally new class of superconductivity with the so-called Bogoliubov Fermi surfaces (BFSs) in this system. However, such an ultranodal pair state requires broken time-reversal symmetry (TRS) in the superconducting state, which has not been observed experimentally. Here, we report muon spin relaxation (µSR) measurements in FeSe1-xSx superconductors for 0 ≤ x ≤ 0.22 covering both orthorhombic (nematic) and tetragonal phases. We find that the zero-field muon relaxation rate is enhanced below the superconducting transition temperature Tc for all compositions, indicating that the superconducting state breaks TRS both in the nematic and tetragonal phases. Moreover, the transverse-field µSR measurements reveal that the superfluid density shows an unexpected and substantial reduction in the tetragonal phase (x > 0.17). This implies that a significant fraction of electrons remain unpaired in the zero-temperature limit, which cannot be explained by the known unconventional superconducting states with point or line nodes. The TRS breaking and the suppressed superfluid density in the tetragonal phase, together with the reported enhanced zero-energy excitations, are consistent with the ultranodal pair state with BFSs. The present results reveal two different superconducting states with broken TRS separated by the nematic critical point in FeSe1-xSx, which calls for the theory of microscopic origins that account for the relation between nematicity and superconductivity.

Supercurrent diode effect and finite-momentum superconductors.

SignificanceOur work shows a fascinating application of finite-momentum superconductivity, the supercurrent diode effect, which is being reported in a growing number of experiments. We show that, under external magnetic field, Cooper pairs can acquire finite momentum so that critical currents in the direction parallel and antiparallel to the Cooper pair momentum become unequal.

Spin-triplet superconductivity from excitonic effect in doped insulators.

SignificanceWe present a mechanism for unconventional superconductivity in doped band insulators, where short-ranged pairing interaction arises from Coulomb repulsion due to virtual interband or excitonic processes. Remarkably, electron pairing is found upon infinitesimal doping, giving rise to Bose-Einstein condensate (BEC)-Bardeen-Cooper-Schrieffer (BCS) crossover at low density. Our theory explains puzzling behaviors of superconductivity and predicts spin-triplet pairing in electron-doped ZrNCl and WTe2.

Multicomponent odd-parity superconductivity in UAu2 at high pressure.

We report that high-quality single crystals of the hexagonal heavy fermion material uranium diauride (UAu2) become superconducting at pressures above 3.2 GPa, the pressure at which an unusual antiferromagnetic state is suppressed. The antiferromagnetic state hosts a marginal fermi liquid and the pressure evolution of the resistivity within this state is found to be very different from that approaching a standard quantum phase transition. The superconductivity that appears above this transition survives in high magnetic fields with a large critical field for all field directions. The critical field also has an unusual angle dependence suggesting that the superconductivity may have an order parameter with multiple components. An order parameter consistent with these observations is predicted to host half-quantum vortices (HQVs). Such vortices can be topologically entangled and have potential applications in quantum computing.

Differentiated roles of Lifshitz transition on thermodynamics and superconductivity in La2-xSrxCuO4.

The effect of Lifshitz transition on thermodynamics and superconductivity in hole-doped cuprates has been heavily debated but remains an open question. In particular, an observed peak of electronic specific heat is proposed to originate from fluctuations of a putative quantum critical point p* (e.g., the termination of pseudogap at zero temperature), which is close to but distinguishable from the Lifshitz transition in overdoped La-based cuprates where the Fermi surface transforms from hole-like to electron-like. Here we report an in situ angle-resolved photoemission spectroscopy study of three-dimensional Fermi surfaces in La2-xSrxCuO4 thin films (x = 0.06 to 0.35). With accurate kz dispersion quantification, the said Lifshitz transition is determined to happen within a finite range around x = 0.21. Normal state electronic specific heat, calculated from spectroscopy-derived band parameters, reveals a doping-dependent profile with a maximum at x = 0.21 that agrees with previous thermodynamic microcalorimetry measurements. The account of the specific heat maximum by underlying band structures excludes the need for additionally dominant contribution from the quantum fluctuations at p*. A d-wave superconducting gap smoothly across the Lifshitz transition demonstrates the insensitivity of superconductivity to the dramatic density of states enhancement.

Phase diagram of superconductivity in the integer quantum Hall regime.

An interplay between pairing and topological orders has been predicted to give rise to superconducting states supporting exotic emergent particles, such as Majorana particles obeying non-Abelian braid statistics. We consider a system of spin polarized electrons on a Hofstadter lattice with nearest-neighbor attractive interaction and solve the mean-field Bogoliubov-de Gennes equations in a self-consistent fashion, leading to gauge-invariant observables and a rich phase diagram as a function of the chemical potential, the magnetic field, and the interaction. As the strength of the attractive interaction is increased, the system first makes a transition from a quantum Hall phase to a skyrmion lattice phase that is fully gapped in the bulk but has topological chiral edge current, characterizing a topologically nontrivial state. This is followed by a vortex phase in which the vortices carrying Majorana modes form a lattice; the spectrum contains a low-energy Majorana band arising from the coupling between neighboring vortex-core Majorana modes but does not have chiral edge currents. For some parameters, a dimer vortex lattice occurs with no Majorana band. The experimental feasibility and the observable consequences of skyrmions as well as Majorana modes are indicated.

Mechanism of superconductivity in the Hubbard model at intermediate interaction strength.

We study the fluctuations responsible for pairing in the d-wave superconducting state of the two-dimensional Hubbard model at intermediate coupling within a cluster dynamical mean-field theory with a numerically exact quantum impurity solver. By analyzing how momentum- and frequency-dependent fluctuations generate the d-wave superconducting state in different representations, we identify antiferromagnetic fluctuations as the pairing glue of superconductivity in both the underdoped and the overdoped regime. Nevertheless, in the intermediate coupling regime, the predominant magnetic fluctuations may differ significantly from those described by conventional spin fluctuation theory.

Phase tuning of multiple Andreev reflections of Dirac fermions and the Josephson supercurrent in Al-MoTe2-Al junctions.

When an electron is incident on a superconductor from a metal, it is reflected as a hole in a process called Andreev reflection. If the metal N is sandwiched between two superconductors S in an SNS junction, multiple Andreev reflections (MARs) occur. We have found that, in SNS junctions with high transparency ([Formula: see text]) based on the Dirac semimetal MoTe2, the MAR features are observed with exceptional resolution. By tuning the phase difference [Formula: see text] between the bracketing Al superconductors, we establish that the MARs coexist with a Josephson supercurrent [Formula: see text]. As we vary the junction voltage V, the supercurrent amplitude [Formula: see text] varies in step with the MAR order n, revealing a direct relation between them. Two successive Andreev reflections serve to shuttle a Cooper pair across the junction. If the pair is shuttled coherently, it contributes to [Formula: see text]. The experiment measures the fraction of pairs shuttled coherently vs. V. Surprisingly, superconductivity in MoTe2 does not affect the MAR features.