  A relationship is derived between differences in electric polarization
between bands and the "shift vector" that controls part of a material's bulk
photocurrent, then demonstrated in several models. Electric polarization has a
quantized gauge ambiguity and is normally observed at surfaces via the surface
charge density, while shift current is a bulk property and is described by
shift vector gauge invariant at each point in momentum space. They are
connected because the same optical transitions that are described in shift
currents pick out a relative gauge between valence and conduction bands. We
also discuss subtleties arising when there are points at the Brillouin zone
where optical transitions are absent. We conclude that two-dimensional
materials with significant interband polarization differences should have high
bulk photocurrent, meaning that the modern theory of polarization can be used
as a straightforward way to search for bulk photovoltaic material candidates.
