  The nonlinear shift current, also known as the bulk photovoltaic current
generated by linearly polarized light, has long been known to be absent in
crystals with inversion symmetry. Here we argue that a non-zero shift current
in centrosymmetric crystals can be activated by a photon-drag effect.
Photon-drag shift current proceeds from a `shift current dipole' (a geometric
quantity characterizing interband transitions) and manifests a purely
transverse response in centrosymmetric crystals. This transverse nature
proceeds directly from the shift-vector's pseudovector nature under mirror
operation and underscores its intrinsic geometric origin. Photon-drag shift
current can greatly enhanced by coupling to polaritons and provides a new and
sensitive tool to interrogate the subtle interband coherences of materials with
inversion symmetry previously thought to be inaccessible via photocurrent
probes.
