Vortex-enhanced photovoltaic current in disordered topological materials

In disordered topological materials, real-space crystalline defects interplay with momentum-space wave function singularities to \textit{enhance} the bulk photovoltaic current. What's singular is the interband Berry phase, or equivalently the phase of the \textit{optical} dipole matrix element, which has a \textit{vortex} structure in momentum space. Such \textit{optical vorticity} is guaranteed to exist in all topological materials associated with nontrivial Chern numbers. These vortices enhance electron-impurity skew scattering, which manifests as a ballistic photovoltaic current that is sensitive to (a) the topological material class, (b) the symmetry class of crystalline defects, and (c) the light polarization. This sensitivity manifests in two ways: firstly, by (a-c)-dependent frequency exponents for the photovoltaic current $\propto \omega^{\text{exponent}}$ in topological semimetals, with $\omega$ the frequency of the light source. Secondly, by (a-c)-dependent constraints of the bulk photovoltaic tensor, which are explainable only by emergent, \textit{magnetic} symmetries of \textit{time-reversal-invariant} topological materials. These ideas are concretized by case studies on multifold fermions, 3D $m$-order Weyl semimetals and 2D $n$-order Dirac systems, which include $n$-layer rhombohedral graphene, transition metal dichalcogenides, and topological surface states. Theoretical guidance is provided for a tri-pronged experimental program that combines frequency-tuned photoconductivity measurements, defect characterization and defect engineering.