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This paper decomposes the shift current conductivity into contributions from interband Berry curvature and quantized point charges at transition dipole zeros, providing an exact, frequency-dependent expression. By analyzing graphene-Haldane and biased AB bilayers, it demonstrates that the sign of the photocurrent is controlled by the winding number of band-edge charges, not solely the Chern number, especially when trigonal warping is present. This reveals that a band-edge charge, independent of topological invariants, can dictate photocurrent sign reversals under specific band-edge conditions.
Photocurrent sign reversals are dictated by the winding of band-edge charges, not just the Chern number, especially with trigonal warping.
Does any integer survive in the shift current, and does the Chern number control its sign? We show that the shift vector is a singular field on the Brillouin torus. Its curl has two sources: the interband Berry curvature and quantised point charges at the zeros of the transition dipole. Inverting this relation gives an exact decomposition of the shift conductivity, valid at every frequency, into one sector linear in the integer charges and three continuous sectors. As a testing ground, we take a graphene-Haldane bilayer: a model that lets us sweep the interband Chern number through five values at fixed gap to isolate its role. We also test the formalism against the time-reversal-symmetric biased AB bilayer. Whenever a charge sits at the band edge, and trigonal warping is present, the integer sector alone accounts for the band-edge peak. The relevant integer is not the Chern number but the winding of that single charge. Its sign, combined with a valley-dependent profile, sets the sign of the photocurrent. In these bilayers, sign reversals across topological transitions follow this winding; the invariant changes with it only when the same gap closing does both. A band-edge charge needs no invariant. It only requires that the two band-edge sublattices not be connected by the nearest-neighbour hopping, and trigonal warping makes it visible.