  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 at the level 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, gapped phases of TBG exhibit
exponentially decaying specific heat capacity and exponential decay in
out-of-time-ordered correlators (OTOC). 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.
