  The bulk photovoltaic effect (BPVE) refers to the phenomenon of generating
photocurrent or photovoltage in homogeneous noncentrosymmetric materials under
illumination, and the intrinsic contribution to the BPVE is known as the shift
current effect. We calculate the shift current conductivities of the
ferroelectric SnTe monolayer using first-principles methods. We find that the
monolayer SnTe has giant shift-current conductivity near the valley points.
More remarkably, the linear optical absorption coefficient at this energy is
very small, and therefore leads to an enormous Glass coefficient that is four
orders of magnitude larger than that of BaTiO$_3$. The unusual shift-current
effects are further investigated using a three-band model. We find that the
giant shift current conductivities and Glass coefficient are induced by the
nontrivial energy band geometries near the valley points, where the
shift-vector diverges. This is a prominent example that the band geometry can
play essential roles in the fundamental properties of solids.
