Quantum information scrambling in disordered magic-angle twisted bilayer graphene

Two-dimensional (2d) Fermi liquid with a dispersive band in the presence of impurities remains to behave as Fermi liquid in the ballistic regime. However, we will show that the presence of impurities of even smooth disorder in the 2d flatband fermionic system immediately causes quantum chaos with a linear-T Lyapunov exponent for out-of-time-ordered correlators (OTOC). We use exact diagonalization and stochastic expansion to study magic-angle twisted bilayer graphene (MATBG) on a disordered substrate. Strong disorder drives the interacting flatbands into a random network of weakly coupled Sachdev-Ye-Kitaev (SYK) bundles, stabilizing an emergent quantum chaotic strange metal (SM) phase of disordered MATBG that exhibits the absence of quasiparticles. The Gaussian orthogonal ensemble dominates its long-time chaotic dynamics, whereas fast quantum scrambling appears in the short-time dynamics. In weak disorder regions, disordered MATBG exhibits exponentially decaying specific heat capacity and exponential decay in OTOC. The latter follows the Larkin-Ovchinnikov behavior, suggesting the onset of a superconducting transition upon doping the system. A finite-temperature phase diagram is proposed for disordered MATBG, and the experimental consequences of the emergent SM phase are discussed.