Sector-Resolved Winding Selection Rules for Structured-Light-Driven dc Currents

Structured light can generate electronic dc currents with azimuthal winding, yet the rules governing their winding order $m$ remain unclear. Here we identify sector-resolved winding selection rules using graphene as a clean two-dimensional platform. By decomposing the current response into local and gradient sectors at the current-operator level, we show that the winding order is determined not by the optical orbital angular momentum $\mathrm{\ell }$ alone, but by the angular structure of the corresponding current operators together with projection onto the azimuthal direction. For scalar Laguerre-Gaussian beams, linear polarization yields $m=\mathrm{\mid }\mathrm{\ell }\pm 1\mathrm{\mid }$ in the local sector and $m=\mathrm{\mid }\mathrm{\ell }\mathrm{\mid },\mathrm{\mid }\mathrm{\ell }\pm 2\mathrm{\mid }$ in the gradient sector, whereas circular polarization with helicity $\sigma =\pm 1$ selects $m=\mathrm{\mid }\mathrm{\ell }-\sigma \mathrm{\mid }$ in the local sector and $m=\mathrm{\mid }\mathrm{\ell }+2\sigma \mathrm{\mid }$ in the gradient sector. Numerical time-evolution calculations verify these rules and further show that helicity can select an $m=0$ branch, producing an azimuthally uniform circulating current whose radial profile determines the axial magnetic field $B_z(z)$. Our results provide a sector-resolved organizing principle for classifying and controlling structured-light-driven dc currents with tailored winding structures.