Motivated by recent experiments indicating strong superconductivity and intricate correlated insulating and flavor-polarized physics in mirror-symmetric twisted trilayer graphene, we study the effects of interactions in this system close to the magic
angle, using a combination of analytical and numerical methods. We identify asymptotically exact correlated many-body ground states at all integer filling fractions $ u$ of the flat bands. To determine their fate when moving away from these fine-tuned points, we apply self-consistent Hartree-Fock numerics and analytic perturbation theory, with good agreement between the two approaches. This allows us to construct a phase diagram for the system as a function of $ u$ and the displacement field, the crucial experimental tuning parameter of the system, and study the spectra of the different phases. The phase diagram is dominated by a correlated semimetallic intervalley coherent state and an insulating sublattice-polarized phase around charge neutrality, $ u=0$, with additional spin-polarization being present at quarter ($ u=-2$) or three quarter ($ u=+2$) fillings of the quasi-flat bands. We further study the superconducting instabilities emerging from these correlated states, both in the absence and in the additional presence of electron-phonon coupling, also taking into account possible Wess-Zumino-Witten terms. In the experimentally relevant regime, we find triplet pairing to dominate, possibly explaining the observed violation of the Pauli limit. Our results have several consequences for experiments as well as future theoretical work and illustrate the rich physics resulting from the interplay of almost flat bands and dispersive Dirac cones in twisted trilayer graphene.
We describe a solvable model of a quantum transition in a single band model involving a change in the size of the electron Fermi surface without any symmetry breaking. In a model with electron density $1-p$, we find a large Fermi surface state with t
he conventional Luttinger volume $1-p$ of electrons for $p>p_c$, and a first order transition to a small Fermi surface state with a non-Luttinger volume $p$ of holes for $p<p_c$. As required by extended Luttinger theorems, the small Fermi surface state also has fractionalized spinon excitations. The model has electrons with strong local interactions in a single band; after a canonical transformation, the interactions are transferred to a coupling to two layers of ancilla qubits, as proposed by Zhang and Sachdev (Phys. Rev. Research ${bf 2}$, 023172 (2020)). Solvability is achieved by employing random exchange interactions within the ancilla layers, and taking the large $M$ limit with SU($M$) spin symmetry, as in the Sachdev-Ye-Kitaev models. The local electron spectral function of the small Fermi surface phase displays a particle-hole asymmetric pseudogap, and maps onto the spectral function of a lightly doped Kondo insulator of a Kondo-Heisenberg lattice model. We discuss connections to the physics of the hole-doped cuprates: the asymmetric pseudogap observed in STM, and the sudden change from incoherent to coherent anti-nodal spectra observed recently in photoemission. A holographic analogy to wormhole transitions between multiple black holes is briefly noted.
Motivated by recent experiments on the phonon contribution to the thermal Hall effect in the cuprates, we present an analysis of chiral phonon transport. We assume the chiral behavior arises from a non-zero phonon Hall vicosity, which is likely induc
ed by the coupling to electrons. Phonons with a non-zero phonon Hall viscosity have an intrinsic thermal Hall conductivity, but Chen et al. (Phys. Rev. Lett. 124, 167601 (2020)) have argued that a significantly larger thermal Hall conductivity can arise from an extrinsic contribution which is inversely proportional to the density of impurities. We solve the Boltzmann equation for phonon transport and compute the temperature ($T$) dependence of the thermal Hall conductivity originating from skew scattering off point-like impurities. We find that the dominant source for thermal Hall transport is an interference between impurity skew scattering channels with opposite parity. The thermal Hall conductivity $sim T^{d+2}$ at low $T$ in $d$ dimensions, and has a window of $T$-independent behavior for $T > T_{rm imp}$, where $T_{rm imp}$ is determined by the ratio of scattering potentials with opposite parity. We also consider the role of non-specular scattering off the sample boundary, and find that it leads to negligible corrections to thermal Hall transport at low $T$.
Anomalous metals are observed in numerous experiments on disordered two-dimensional systems proximate to superconductivity. A characteristic feature of an anomalous metal is that its low temperature conductivity has a weakly temperature dependent val
ue, significantly higher than that of a disordered Fermi liquid. We propose a dynamical mean-field model of an anomalous metal: interacting electrons similar in structure to that of the well-studied universal Hamiltonian of mesoscopic metallic grains, but with independent random interactions between pairs of sites, involving Cooper pair hopping and spin exchange. We find evidence for critical anomalous phases or points between a superconducting phase and a disordered Fermi liquid phase in this model. Our results are obtained by a renormalization group analysis in a weak coupling limit, and a complementary solution at large $M$ when the spin symmetry is generalized to USp($M$). The large $M$ limit describes the anomalous metal by fractionalization of the electron into spinons, holons, and doublons, with these partons forming critical non-Fermi liquids in the Sachdev-Ye-Kitaev class. We compute the low temperature conductivity in the large $M$ limit, and find temperature-independent values moderately enhanced from that in the disordered metal.
We present numerical solutions of the spectral functions of $t$-$J$ models with random and all-to-all exchange and global SU($M$) spin rotation symmetry. The solutions are obtained from the saddle-point equations of the large volume limit, followed b
y the large $M$ limit. These saddle point equations involve Greens functions for fractionalized spinons and holons carrying emergent U(1) gauge charges, obeying relations similar to those of the Sachdev-Ye-Kitaev (SYK) models. The low frequency spectral functions are compared with an analytic analysis of the operator scaling dimensions, with good agreement. We also compute the low frequency and temperature behavior of gauge-invariant observables: the electron Greens function, the local spin susceptibility and the optical conductivity; along with the temperature dependence of the d.c. resistivity. The time reparameterization soft mode (equivalent to the boundary graviton in holographically dual models of two-dimensional quantum gravity) makes important contributions to all observables, and provides a linear-in-temperature contribution to the d.c. resistivity.
We study the low frequency spectra of complex Sachdev-Ye-Kitaev (SYK) models at general densities. The analysis applies also to SU($M$) magnets with random exchange at large $M$. The spectral densities are computed by numerical analysis of the saddle
point equations on the real frequency ($omega$) axis at zero temperature ($T$). The asymptotic low $omega$ behaviors are found to be in excellent agreement with the scaling dimensions of irrelevant operators which perturb the conformally invariant critical states. Of possible experimental interest is our computation of the universal spin spectral weight of the SU($M$) magnets at low $omega$ and $T$: this includes a contribution from the time reparameterization mode, which is the boundary graviton of the holographic dual. This analysis is extended to a random $t$-$J$ model in a companion paper.
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 temperatu
res. 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.
A previous work (Joshi et al., arXiv:1912.08822) found a deconfined critical point at non-zero doping in a $t$-$J$ model with all-to-all and random hopping and spin exchange, and argued for its relevance to the phenomenology of the cuprates. We exten
d this model to include all-to-all and random density-density interactions of mean-square strength $K$. In a fixed realization of the disorder, and for specific values of the hopping, exchange, and density interactions, the model is supersymmetric; but, we find no supersymmetry after independent averages over the interactions. Using the previously developed renormalization group analysis, we find a new fixed point at non-zero $K$. However, this fixed point is unstable towards the previously found fixed point at $K=0$ in our perturbative analysis. We compute the exponent characterizing density fluctuations at both fixed points: this exponent determines the spectrum of electron energy-loss spectroscopy.
We consider 2+1 dimensional conformal gauge theories coupled to additional degrees of freedom which induce a spatially local but long-range in time $1/(tau-tau)^2$ interaction between gauge-neutral local operators. Such theories have been argued to d
escribe the hole-doped cuprates near optimal doping. We focus on a SU(2) gauge theory with $N_h$ flavors of adjoint Higgs fields undergoing a quantum transition between Higgs and confining phases: the $1/(tau-tau)^2$ interaction arises from a spectator large Fermi surface of electrons. The large $N_h$ expansion leads to an effective action containing fields which are bilocal in time but local in space. We find a strongly-coupled fixed point at order $1/N_h$, with dynamic critical exponent $z > 1$. We show that the entropy preserves hyperscaling, but nevertheless leads to a linear in temperature specific heat with a co-efficient which has a finite enhancement near the quantum critical point.
We propose a general theoretical framework, using two layers of ancilla qubits, for deconfined criticality between a Fermi liquid with a large Fermi surface, and a pseudogap metal with a small Fermi surface of electron-like quasiparticles. The pseudo
gap metal can be a magnetically ordered metal, or a fractionalized Fermi liquid (FL*) without magnetic order. A critical ghost Fermi surface emerges (alongside the large electron Fermi surface) at the transition, with the ghost fermions carrying neither spin nor charge, but minimally coupled to $(U(1) times U(1))/Z_2$ or $(SU(2) times U(1))/Z_2$ gauge fields. The $(U(1) times U(1))/Z_2$ case describes simultaneous Kondo breakdown and onset of magnetic order: the two gauge fields induce nearly equal attractive and repulsive interactions between ghost Fermi surface excitations, and this competition controls the quantum criticality. Away from the transition on the pseudogap side, the ghost Fermi surface absorbs part of the large electron Fermi surface, and leads to a jump in the Hall co-efficient. We also find an example of an unnecessary quantum critical point between a metal with spin density wave order, and a metal with local moment magnetic order. The ghost fermions contribute an enhanced specific heat near the transition, and could also be detected in other thermal probes. We relate our results to the phases of correlated electron compounds.
