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Superconductivity was recently discovered in rhombohedral trilayer graphene (RTG) in the absence of a moiré potential. Superconductivity is observed proximate to a metallic state with reduced isospin symmetry, but it remains unknown whether this is a coincidence or a key ingredient for superconductivity. Using a Hartree-Fock analysis and constraints from experiments, we argue that the symmetry breaking is inter-valley coherent (IVC) in nature. We evaluate IVC fluctuations as a possible pairing glue, and find that they lead to chiral unconventional superconductivity when the fluctuations are strong. We further elucidate how the inter-valley Hund’s coupling determines the spin-structure of the IVC ground state and breaks the degeneracy between spin-singlet and triplet superconductivity. Remarkably, if the normal state is spin-unpolarized, we find that a ferromagnetic Hund’s coupling favors spin-singlet superconductivity, in agreement with experiments. Instead, if the normal state is spin-polarized, then IVC fluctuations lead to spin-triplet pairing. Trilayer graphene was recently shown to exhibit superconductivity without a Moire pattern that had proved important in tuning superconductivity in bilayer graphene. Here, the authors explore correlated metallic phases and the pairing mechanism of superconductivity in trilayer graphene, and show that intervalley coherent fluctuations can act as a pairing glue, giving rise to chiral unconventional superconductivity.

Using determinantal quantum Monte Carlo, we compute the properties of a lattice model with spin ½ itinerant electrons tuned through a quantum phase transition to an Ising nematic phase. The nematic fluctuations induce superconductivity with a broad dome in the superconducting Tc enclosing the nematic quantum critical point. For temperatures above Tc , we see strikingly non-Fermi liquid behavior, including a “nodal–antinodal dichotomy” reminiscent of that seen in several transition metal oxides. In addition, the critical fluctuations have a strong effect on the lowfrequency optical conductivity, resulting in behavior consistent with “bad metal” phenomenology.

We construct examples of translationally invariant solvable models of strongly correlated metals, composed of lattices of Sachdev-Ye-Kitaev dots with identical local interactions. These models display crossovers as a function of temperature into regimes with local quantum criticality and marginal-Fermi-liquid behavior. In the marginal-Fermi-liquid regime, the dc resistivity increases linearly with temperature over a broad range of temperatures. By generalizing the form of interactions, we also construct examples of non-Fermi liquids with critical Fermi surfaces. The self-energy has a singular frequency dependence but lacks momentum dependence, reminiscent of a dynamical mean-field-theory-like behavior but in dimensionsd<∞. In the low-temperature and strong-coupling limit, a heavy Fermi liquid is formed. The critical Fermi surface in the non-Fermi-liquid regime gives rise to quantum oscillations in the magnetization as a function of an external magnetic field in the absence of quasiparticle excitations. We discuss the implications of these results for local quantum criticality and for fundamental bounds on relaxation rates. Drawing on the lessons from these models, we formulate conjectures on coarse-grained descriptions of a class of intermediate-scale non-Fermi-liquid behavior in generic correlated metals.

The rich phenomenology of twisted bilayer graphene (TBG) near the magic angle is believed to arise from electron correlations in topological flat bands. An unbiased approach to this problem is highly desirable, but also particularly challenging, given the multiple electron flavors, the topological obstruction to defining tight-binding models, and the long-ranged Coulomb interactions. While numerical simulations of realistic models have thus far been confined to zero temperature, typically excluding some spin or valley species, analytic progress has relied on fixed point models away from the realistic limit. Here, we present unbiased Monte Carlo simulations of realistic models of magic-angle TBG at charge neutrality. We establish the absence of a sign problem for this model in a momentum-space approach and describe a computationally tractable formulation that applies even on breaking chiral symmetry and including band dispersion. Our results include (i) the emergence of an insulating Kramers intervalley coherent ground state in competition with a correlated semimetal phase, (ii) detailed temperature evolution of order parameters and electronic spectral functions that reveal a “pseudogap” regime, in which gap features are established at a higher temperature than the onset of order, and (iii) predictions for electronic tunneling spectra and their evolution with temperature. Our results pave the way towards uncovering the physics of magic-angle graphene through exact simulations of over a hundred electrons across a wide temperature range.

Recently, several authors have investigated topological phenomena in periodically driven systems of noninteracting particles. These phenomena are identified through analogies between the Floquet spectra of driven systems and the band structures of static Hamiltonians. Intriguingly, these works have revealed phenomena that cannot be characterized by analogy to the topological classification framework for static systems. In particular, in driven systems in two dimensions (2D), robust chiral edge states can appear even though the Chern numbers of all the bulk Floquet bands are zero. Here, we elucidate the crucial distinctions between static and driven 2D systems, and construct a new topological invariant that yields the correct edge-state structure in the driven case. We provide formulations in both the time and frequency domains, which afford additional insight into the origins of the “anomalous” spectra that arise in driven systems. Possibilities for realizing these phenomena in solid-state and cold-atomic systems are discussed.

The quantum theory of antiferromagnetism in metals is necessary for our understanding of numerous intermetallic compounds of widespread interest. In these systems, a quantum critical point emerges as external parameters (such as chemical doping) are varied. Because of the strong coupling nature of this critical point and the \"sign problem\" plaguing numerical quantum Monte Carlo (QMC) methods, its theoretical understanding is still incomplete. Here, we show that the universal low-energy theory for the onset of antiferromagnetism in a metal can be realized in lattice models, which are free from the sign problem and hence can be simulated efficiently with QMC. Our simulations show Fermi surface reconstruction and unconventional spin-singlet superconductivity across the critical point.

We consider a two-dimensional electron gas with strong spin-orbit coupling contacted by two superconducting leads, forming a Josephson junction. We show that in the presence of an in-plane Zeeman field, the quasi-one-dimensional region between the two superconductors can support a topological superconducting phase hosting Majorana bound states at its ends. We study the phase diagram of the system as a function of the Zeeman field and the phase difference between the two superconductors (treated as an externally controlled parameter). Remarkably, at a phase difference of π , the topological phase is obtained for almost any value of the Zeeman field and chemical potential. In a setup where the phase is not controlled externally, we find that the system undergoes a first-order topological phase transition when the Zeeman field is varied. At the transition, the phase difference in the ground state changes abruptly from a value close to zero, at which the system is trivial, to a value close to π , at which the system is topological. The critical current through the junction exhibits a sharp minimum at the critical Zeeman field and is therefore a natural diagnostic of the transition. We point out that in the presence of a symmetry under a mirror reflection followed by time reversal, the system belongs to a higher symmetry class, and the phase diagram as a function of the phase difference and the Zeeman field becomes richer.

Charge carriers in magic-angle graphene come in eight flavours described by a combination of their spin, valley and sublattice polarizations. When inversion and time-reversal symmetries are broken, this ‘flavour’ degeneracy can be lifted, and their corresponding bands can be sequentially filled. Due to their non-trivial band topology and Berry curvature, each band is classified by a topological Chern number C , leading to quantum anomalous Hall and Chern insulator states. Using a scanning superconducting quantum interference device on a tip, we image the nanoscale equilibrium orbital magnetism induced by the Berry curvature, the polarity of which is governed by C , and detect its two constituent components associated with the drift and self-rotation of the electronic wavepackets. At integer filling v  = 1, we observe a zero-field Chern insulator, which—rather than being described by a global topologically invariant C —forms a mosaic of microscopic patches of C  = −1, 0 or 1. On further filling, we find a first-order phase transition due to the recondensation of electrons from valley K to K′, leading to irreversible flips of the local Chern number and magnetization, as well as to the formation of valley domain walls, giving rise to hysteretic anomalous Hall resistance. Topological states characterized by Chern numbers are usually considered to be the global properties of a material. Now a spatial patchwork of different Chern insulator states is imaged in twisted bilayer graphene.

Majorana zero modes—quasiparticle states localized at the boundaries of topological superconductors—are expected to be ideal building blocks for fault-tolerant quantum computing 1 , 2 . Several observations of zero-bias conductance peaks measured by tunnelling spectroscopy above a critical magnetic field have been reported as experimental indications of Majorana zero modes in superconductor–semiconductor nanowires 3 – 8 . On the other hand, two-dimensional systems offer the alternative approach of confining Majorana channels within planar Josephson junctions, in which the phase difference φ between the superconducting leads represents an additional tuning knob that is predicted to drive the system into the topological phase at lower magnetic fields than for a system without phase bias 9 , 10 . Here we report the observation of phase-dependent zero-bias conductance peaks measured by tunnelling spectroscopy at the end of Josephson junctions realized on a heterostructure consisting of aluminium on indium arsenide. Biasing the junction to φ  ≈ π reduces the critical field at which the zero-bias peak appears, with respect to φ  = 0. The phase and magnetic-field dependence of the zero-energy states is consistent with a model of Majorana zero modes in finite-size Josephson junctions. As well as providing experimental evidence of phase-tuned topological superconductivity, our devices are compatible with superconducting quantum electrodynamics architectures 11 and are scalable to the complex geometries needed for topological quantum computing 9 , 12 , 13 . Evidence is found for phase-tunable Majorana zero modes in scalable two-dimensional Josephson junctions produced by top-down fabrication.

We show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.