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Abstract:

We use several techniques to probe the wave functions proposed to describe the A phases by Das, Das, and Mandal [Phys. Rev. Lett. 131, 056202 (2023); Phys. Rev. Lett. 132, 106501 (2024); Phys. Rev. B 110, L121303 (2024).]. As opposed to representing fractional quantum Hall liquids, we find these wave functions to describe states that clearly display strong phase separation. In the process of exploring these wave functions, we have also constructed several new methods for diagnosing phase separation and generating such wave functions numerically. Finally, we uncover a new property of entanglement spectra that can be used as a check for the accuracy of numerics.

Abstract:

A striking series of experiments have observed superconductivity in Bernal-stacked bilayer graphene (BBG) when the energy bands are flattened by applying an electrical displacement field. Intriguingly, superconductivity manifests only at nonzero magnetic fields, or when spin-orbit coupling is induced in BBG by coupling to a substrate. We present detailed functional renormalization group and random-phase approximation calculations that provide a unified explanation for the superconducting mechanism in both cases. Both calculations yield a purely electronic 𝑝-wave instability of the Kohn-Luttinger type. The latter can be enhanced either by magnetic fields or Ising spin-orbit coupling, naturally explaining the behavior seen in experiments.

Abstract:

We consider a refined version of the string-net model which assigns a different energy cost to each plaquette excitation. Using recent exact calculations of the energy-level degeneracies we compute the partition function of this model and investigate several thermodynamical quantities. In the thermodynamic limit, we show that the partition function is dominated by the contribution of special particles, dubbed pure fluxons, which trivially braid with all other (product of) fluxons. We also analyze the behavior of Wegner-Wilson loops associated to excitations and show that they obey an area law, indicating confinement, for any finite temperature except for pure fluxons that always remain deconfined. Finally, using a recently proposed conjecture, we compute the topological mutual information at finite temperature, which features a nontrivial scaling between system size and temperature.

Abstract:

Recent scanning tunneling microscopy experiments in twisted bilayer [K. P. Nuckolls et al., Nature (London) 620, 525 (2023)] and trilayer [H. Kim et al., Nature (London) 623, 942 (2023)] graphene have revealed the ubiquity of Kekulé charge-density wave order in magic-angle graphene. Most samples are moderately strained and show “incommensurate Kekulé spiral” (IKS) order involving a graphene-scale charge density distortion uniaxially modulated on the scale of the moiré superlattice, in accord with theoretical predictions. However, ultralow strain bilayer samples instead show graphene-scale Kekulé charge order that is uniform on the moiré scale. This order, especially prominent near filling factor 𝜈=−2, is unanticipated by theory which predicts a time-reversal breaking Kekulé current order at low strain. We show that including the coupling of moiré electrons to graphene-scale optical zone-corner (ZC) phonons stabilizes a uniform Kekulé charge ordered state at |𝜈|=2 with a quantized topological (spin or anomalous Hall) response. Our work clarifies how this phonon-driven selection of electronic order emerges in the strong-coupling regime of moiré graphene.