  The nonlinear optical responses from topological semimetals are crucial in
both understanding the fundamental properties of quantum materials and
designing next-generation light-sensors or solar-cells. However, previous work
was focusing on the optical effects from bulk states only, disregarding
topological surface responses. Here we propose a new (hitherto unknown)
surface-only topological photocurrent response from chiral Fermi arcs. Using
the ideal topological chiral semimetal RhSi as a representative, we
quantitatively compute the topologically robust photocurrents from Fermi arcs
on different surfaces. By rigorous crystal symmetry analysis, we demonstrate
that Fermi arc photocurrents can be perpendicular to the bulk injection
currents regardless of the choice of materials' surface. We then generalize
this finding to all cubic chiral space groups and predict material candidates.
Our theory reveals a powerful notion where common crystalline-symmetry can be
used to induce universal topological responses as well as making it possible to
completely disentangle bulk and surface topological responses in many
conducting material families.
