Strange metal phase of disordered magic-angle twisted bilayer graphene at low temperatures: From flat bands to weakly coupled Sachdev-Ye-Kitaev bundles

We use stochastic expansion and exact diagonalization to study magic-angle twisted bilayer graphene (TBG) on a disordered substrate. We show that the substrate-induced strong Coulomb disorder in TBG with the chemical potential at the level of the flat bands drives the system to a network of weakly coupled Sachdev-Ye-Kitaev (SYK) bundles, stabilizing an emergent quantum chaotic strange metal (SM) phase of TBG that exhibits the absence of quasiparticles. The Gaussian orthogonal ensemble dominates TBG's long-time chaotic dynamics at strong disorder, whereas fast quantum scrambling appears in the short-time dynamics. In weak disorder, gapped phases of TBG exhibit exponentially decaying specific heat capacity and exponential decay in out-of-time-ordered correlators (OTOCs). This is the system behavior in correlated insulator and superconducting phases, in agreement with the corresponding Larkin-Ovchinnikov result for correlators. The result suggests a low-temperature transition from the superconducting and correlated insulating phases into the strange metal upon increasing the disorder strength. We propose a finite-temperature phase diagram for Coulomb-disordered TBG and discuss the experimental consequences of the emergent SM phase.