  Nonlinear optical (NLO) responses of topological materials are under active
research in recent years. Yet by far, most studies focused on the bulk
properties, whereas the surface effects and the difference between surface and
bulk responses have not been systematically studied. Here we develop a generic
Green's function framework to investigate the surface NLO properties of
topological materials. The Green's function framework can naturally incorporate
many-body effects and can be easily extended to high-order NLO responses. Using
Td-WTe2 as an example, we reveal that the surface can behave disparately from
the bulk under light illumination. Remarkably, the shift and circular currents
on the surface can flow in opposite directions to those in the bulk interior.
Moreover, the light-induced spin current on the surface can be orders of
magnitude stronger than its bulk counterpart. We also study the responses under
inhomogeneous field and higher-order NLO effect, which are all distinct on the
surface. These anomalous surface NLO responses suggest that light can be a
valuable tool for probing the surface states of topological materials. On the
other hand, the surface effects shall be prudently considered when
investigating the optical properties of topological materials, especially if
the material is of nanoscale and/or the light penetration depth is small.
