  Time crystals form when arbitrary physical states of a periodically driven
system spontaneously break discrete time-translation symmetry. We introduce
one-dimensional time-crystalline topological superconductors, for which
time-translation symmetry breaking and topological physics
intertwine---yielding anomalous Floquet Majorana modes that are not possible in
free-fermion systems. Such a phase exhibits a bulk magnetization that returns
to its original form after two drive periods, together with Majorana end modes
that recover their initial form only after four drive periods. We propose
experimental implementations and detection schemes for this new state.

Mesoscale and Nanoscale Physics