Chirality rules for optical vortices in rhombohedral graphene multilayers

Abstract

Optical zeros are momenta where the interband dipole vanishes. The dipole phase winds around each of them by an integer, so they are vortices of the resonant optical response with a conserved charge. We show that in rhombohedral graphene multilayers one integer, the stacking chirality $N$, fixes their constellation near the $K$ valley: the total charge per linear polarization is $N-1$ and is conserved under trigonal warping and interlayer bias; for $N\ge3$ the $K$ point stays an exact optical zero, the Bernal bilayer being the only exception; warping places the remaining charge on satellites whose radii scale linearly with the warping; and the charge pinned at $K$ is bias independent for $N\ge4$. A quantized interband character counts the enclosed charge as an integer staircase with steps at these radii, and an interlayer bias drives a satellite through the protected $K$ vortex in the trilayer. The rules survive the remote hoppings of the full tight-binding model and, being integer charges, the corrections that reshape the bands. The same integer sets the magnitude of the response: the band-edge shift current grows linearly with $N$.