  Discrete time crystals (DTCs) are emergent non-equilibrium phases of
periodically driven many-body systems, with potential applications ranging from
quantum computing to sensing and metrology. There has been significant recent
interest in understanding mechanisms leading to DTC formation and a search for
novel DTC phases beyond subharmonic entrainment. Here, we report observation of
multiple DTC phases in a nanoelectromechanical system (NEMS) based on coupled
graphene and silicon nitride membranes. We confirm the time-crystalline nature
of these symmetry broken phases by establishing their many-body characters,
long-range time and spatial order, and rigidity against parameter fluctuation
or noise. Furthermore, we employ controlled mechanical strain to drive the
transitions between phases with different symmetries, thereby mapping the
emergent time-crystalline phase diagram. Overall, our work takes a step towards
establishing time crystals as a system with complexity rivaling that of solid
state crystals.
