  Discrete time crystals (DTCs) are nonequilibrium phases of matter
characterized by robust subharmonic order parameter dynamics. We report a new
type of DTC in a periodically driven surface code, the subharmonic signature of
which is only observable with respect to some nonlocal order parameter. By
modifying the commonly used metrics for characterizing ordinary DTCs, i.e., the
spectral functions, spin-glass order parameters, and two-point correlators, we
numerically investigate the different phases of the proposed system.
Specifically, depending on the system parameters and boundary conditions, we
find that the system may fall into either a "surface code" phase, trivial
paramagnet phase, nonlocal period-doubling DTC phase, or nonlocal
period-quadrupling DTC phase. Our work thus demonstrates the prospect of
exploring topological codes for discovering novel phases of matter.
