We investigate the band structure and topological phase transition of photonic time crystals (PTC)-systems in which the physical parameter varies periodically in time. We find that the topological phase transition of the PTC system can be revealed by the wave vector gap (k-gap) size, which was induced by the temporal refraction and reflection. Interestingly, a temporal zero-averaged refractive index k-gap is obtained when the PTC system includes a dispersive medium. This special k-gap is invariant with modulation time scaling at a given modulation frequency.
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