  As one indispensable type of nonreciprocal mechanism, a system with temporal
modulations is intrinsically open in the physical sense and inevitably
non-Hermitian, but the space and time degrees of freedom are nonseparable in a
large variety of circumstances, which restrains the non-Bloch band theory to
apply. Here, we investigate the spatially photonic crystals (PhCs) composed of
spatiotemporal modulation materials (STMs) and homogeneous media, dubbed as the
STM-PhC, wherein the spatial and temporal modulations are deliberately designed
to be correlated. To bypass the difficulty of the spatiotemporal correlation,
we first employ the effective medium theory to account for the dispersion of
fundamental bands under the influence of Floquet sidebands. Based on the
dynamical degeneracy splitting viewpoint and continuum generalized Brillouin
zone condition, we then analytically give the criteria for the existence of the
non-Hermitian skin effect in the STM. Assisted by developing a numerical method
that embeds the plane wave expansion in the transfer matrix, we establish the
non-Bloch band theory for the low-frequency Floquet bands in the STM-PhCs, in
which the central is the identification of the generalized Brillouin zone. We
finally delve into the topological properties, including non-Bloch Zak phases
and delocalization of topologically edge states. Our work validates that
effective medium assists the non-Bloch band theory applied to the STM-PhCs,
which delivers a prescription to broaden the horizons of non-Bloch theory.
