Strange metal phase of disordered magic-angle twisted bilayer graphene: from flatbands to weakly coupled Sachdev-Ye-Kitaev bundles

We use stochastic expansion and exact diagonalization to study the 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 in the center of the flatbands 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, TBG exhibits exponentially decaying specific heat capacity and exponential decay in out-of-time-ordered correlators. The latter follows the Larkin-Ovchinnikov behavior of the correlator signaling the onset of the formation of a superconducting state. The result suggests the superconducting transition upon doping the system above the charge neutrality and weakening the disorder strength. We propose a finite-temperature phase diagram for Coulomb disordered TBG and discuss the experimental consequences of the emergent SM phase.Comment: 8 pages, 11 figure