Exact vortex decomposition of the shift current
Abstract
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.
Related
- A novel vortex generator for enhancing bileaflet mechanical heart valve performance proposed through detailed hemodynamic and data-driven dynamic mode decomposition studies
- Exact Single-Scale Outer Solution of the Abrikosov Vortex in the Extreme Type-II Limit
- Vortex-mediated spin current injection into two-dimensional superconductor NbSe2
- Vortex-mediated spin current injection into two-dimensional superconductor NbSe ₂
- Quantum-geometric shift of quasiequilibrium: Origin of nonreciprocal current driven by quantum-metric dipole
BibTeX
@misc{schnaidt2026exact,
title = {{Exact vortex decomposition of the shift current}},
author = {Matias Castro Schnaidt and Felipe Perez Riffo and Juan M. Florez and Eric Suarez Morell},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06449},
eprint = {2610.06449},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06449},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact vortex decomposition of the shift current
AU - Matias Castro Schnaidt
AU - Felipe Perez Riffo
AU - Juan M. Florez
AU - Eric Suarez Morell
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06449
UR - https://arxiv.org/abs/2610.06449
AB - 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.
ER -