  We study discrete time crystals (DTCs) in periodically driven quantum
systems, in the presence of non-Markovian dissipation. In contrast to DTCs
observed in earlier works in the presence of Markovian dynamics, using the open
Dicke model in presence of Jaynes-Cummings-like dissipation, we show that
non-Markovian regime can be highly beneficial for stabilizing DTCs over a wide
range of parameter values. This may be attributed to periodically varying
dissipation rates even at long times in the case of non-Markovian dynamics.
Further the Markovian and non-Markovian regimes show sharp distinctions for
intermediate strengths of the dissipator coefficient, with a time-independent
steady-state in the Markovian regime being replaced by varied dynamical phases,
including DTC order, in the non-Markovian regime. We also verify the robustness
of the DTC phase in the non-Markovian regime by introducing errors both in the
Hamiltonian as well as in the dissipation. Our study shows the possibility of
using DTC as a probe for non-Markovian dynamics in periodically modulated open
quantum systems, at long times.
