  The bulk-edge correspondence is a fundamental principle of topological wave
physics, which states that the difference in gap Chern numbers between the
interfaced materials is equal to the net number of topological edge modes.
Although this principle works well for periodic photonic topological
insulators, difficulties arise in the case of continuous systems with no
intrinsic periodicity, due to the absence of a finite Brillouin zone, which may
lead to an ill-behaved response for diverging wavenumbers. This problem has
been solved previously by introducing an ad hoc material model including a
spatial cutoff wavenumber. However, this method introduces other difficulties,
such as an unphysical response at large wavenumbers, and the need to
interpolate the interfaced materials permittivity functions. In this work, we
show that the inclusion of realistic spatial dispersion (e.g., hydrodynamic
nonlocality) formally restores the bulk-edge correspondence by avoiding an
unphysical response at large wavenumbers, forming a complete, self-consistent
model. This model clarifies the subtle and rich topological wave physics of
continuous media.
