Quantum oscillations in the hole-doped cuprates and the confinement of spinons.

A long-standing problem in the study of the under-hole-doped cuprates has been the description of the Fermi surfaces underlying the high magnetic field quantum oscillations, and their connection to the higher temperature pseudogap metal. Harrison and Sebastian [ , 226402 (2011)] proposed that the pseudogap "Fermi arcs" are reconstructed into an electron pocket by field-induced charge density wave order. But computations on such a model [Zhang and Mei, , 47008 (2016)] show an unobserved additional oscillation frequency from a Fermi surface arising from the backsides of the hole pockets completing the Fermi arcs.

Nodal band-off-diagonal superconductivity in twisted graphene superlattices.

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 chiral p-wave state exhibits transitions between gapped and nodal regions upon varying the doping.

A model of -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 = 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 -flux per plaquette in the ℤ center of SU(2). This theory has an emergent SO(5) global symmetry and is presumed to confine at low energies to the Néel state.

Critical metallic phase in the overdoped random - model.

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- limit with SU() spin symmetry. The saddle-point equations of this model are similar to approximate dynamic mean-field equations of realistic, nonrandom, - models.

Orderly disorder in magic-angle twisted trilayer graphene.

Magic-angle twisted trilayer graphene (TTG) has recently emerged as a platform to engineer strongly correlated flat bands. We reveal the normal-state structural and electronic properties of TTG using low-temperature scanning tunneling microscopy at twist angles for which superconductivity has been observed. Real trilayer samples undergo a strong reconstruction of the moiré lattice, which locks layers into near-magic-angle, mirror symmetric domains comparable in size with the superconducting coherence length.

Superconductivity, correlated insulators, and Wess-Zumino-Witten terms in twisted bilayer graphene.

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.