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We model the pseudogap state of the hole- and electron-doped cuprates as a metal with hole and/or electron pocket Fermi surfaces. In the absence of long-range antiferromagnetism, such Fermi surfaces violate the Luttinger requirement of enclosing the same area as free electrons at the same density. Using the Ancilla theory of such a pseudogap state, we describe the onset of conventionald-wave superconductivity by the condensation of a chargeeHiggs boson transforming as a fundamental under the emergent SU(2) gauge symmetry of a backgroundπ-flux spin liquid. In all cases, we find that thed-wave superconductor has gapless Bogoliubov quasiparticles at 4 nodal points on the Brillouin zone diagonals with significant velocity anisotropy, just as in the BCS state. This includes the case of the electron-doped pseudogap metal with only electron pockets centered at wavevectors (π, 0), (0, π), and an electronic gap along the zone diagonals. Remarkably, in this case, too, gapless nodal Bogoliubov quasiparticles emerge within the gap at 4 points along the zone diagonals upon the onset of superconductivity.

The superconducting state and mechanism are among the least understood phenomena in twisted graphene systems. Recent tunneling experiments indicate a transition between nodal and gapped pairing with electron filling, which is not naturally understood within current theory. We demonstrate that the coexistence of superconductivity and flavor polarization leads to pairing channels that are guaranteed by symmetry to be entirely band-off-diagonal, with a variety of consequences: most notably, the pairing invariant under all symmetries can have Bogoliubov Fermi surfaces in the superconducting state with protected nodal lines, or may be fully gapped, depending on parameters, and the band-off-diagonal chiralp-wave state exhibits transitions between gapped and nodal regions upon varying the doping. We demonstrate that band-off-diagonal pairing can be the leading state when only phonons are considered, and is also uniquely favored by fluctuations of a time-reversal-symmetric intervalley coherent order motivated by recent experiments. Consequently, band-off-diagonal superconductivity allows for the reconciliation of several key experimental observations in graphene moiré systems.

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 ofN_f= 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 withπ-flux per plaquette in the ℤ₂center of SU(2). This theory has an emergent SO(5)_fglobal symmetry and is presumed to confine at low energies to the Néel state. At nonzero doping (or smaller Hubbard repulsionUat half-filling), we argue that confinement occurs via the Higgs condensation of bosonic chargons carrying fundamental SU(2) gauge charges also moving inπℤ₂-flux. At half-filling, the low-energy theory of the Higgs sector hasN_b= 2 relativistic bosons with a possible emergent SO(5)_bglobal symmetry describing rotations between ad-wave superconductor, period-2 charge stripes, and the time-reversal breaking “d-density wave” state. We propose a conformal SU(2) gauge theory withN_f= 2 fundamental fermions,N_b= 2 fundamental bosons, and a SO(5)_f×SO(5)_bglobal symmetry, which describes a deconfined quantum critical point between a confining state which breaks SO(5)_fand 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 andd-wave superconductivity. A similar theory applies at nonzero doping and largeU, with longer-range couplings of the chargons leading to charge order with longer periods.

We investigate a model of electrons with random and all-to-all hopping and spin exchange interactions, with a constraint of no double occupancy. The model is studied in a Sachdev–Ye–Kitaev-like large-Mlimit with SU(M) spin symmetry. The saddle-point equations of this model are similar to approximate dynamic mean-field equations of realistic, nonrandom,t-Jmodels. We use numerical studies on both real and imaginary frequency axes, along with asymptotic analyses, to establish the existence of a critical non–Fermi-liquid metallic ground state at large doping, with the spin correlation exponent varying with doping. This critical solution possesses a time-reparameterization symmetry, akin to Sachdev–Ye–Kitaev (SYK) models, which contributes a linear-in-temperature resistivity over the full range of doping where the solution is present. It is therefore an attractive mean-field description of the overdoped region of cuprates, where experiments have observed a linear-Tresistivity in a broad region. The critical metal also displays a strong particle–hole asymmetry, which is relevant to Seebeck coefficient measurements. We show that the critical metal has an instability to a low-doping spin-glass phase and compute a critical doping value. We also describe the properties of this metallic spin-glass phase.

Recent experiments on twisted bilayer graphene have shown a high-temperature parent state with massless Dirac fermions and broken electronic flavor symmetry; superconductivity and correlated insulators emerge from this parent state at lower temperatures. We propose that the superconducting and correlated insulating orders are connected by Wess–Zumino–Witten terms, so that defects of one order contain quanta of another order and skyrmion fluctuations of the correlated insulator are a “mechanism” for superconductivity. We present a comprehensive listing of plausible low-temperature orders and the parent flavor symmetry-breaking orders. The previously characterized topological nature of the band structure of twisted bilayer graphene plays an important role in this analysis.