Valley-resolved high harmonics probe symmetry breaking beyond the Dirac cone
Abstract
Low-energy electrons in graphene obey an emergent, rotationally invariant Dirac equation, while the honeycomb lattice enters only through higher-order, symmetry-breaking corrections, the leading one being trigonal warping. This provides a unique solid-state arena to address a cornerstone challenge in quantum gravity: how to detect ultraviolet symmetry-breaking granular corrections, suppressed by a fundamental scale, atop an emergent infrared relativistic continuum. We show that intense counter-rotating ω-2ω fields and valley-resolved high-harmonic generation (HHG) provide such a probe. Within a family of models that interpolates continuously between the isotropic Dirac cone and nearest-neighbour graphene at fixed Fermi velocity, the valley contrast of the harmonic yield vanishes identically in the symmetric theory, grows linearly with the warping coupling, and its valley-even counterpart appears only at second order, as expected from effective-field-theory power counting. The stronger the laser, the farther it drives electrons from the Dirac points, so the laser intensity plays the role of the collision energy. For the fourth harmonic, the leading warping correction alone accounts for the valley contrast of real graphene up to fundamental intensities of about 1011 W/cm2, below the damage threshold of monolayer graphene, whereas the fifth harmonic already reveals higher-order lattice corrections at intensities around 1010 W/cm2. The two harmonics, which rotate in opposite directions, are emitted by opposite valleys. Valley-resolved harmonics are far more sensitive than the residual valley populations, making them a practical detector of lattice-scale physics hidden beneath an emergent Dirac theory.
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BibTeX
@misc{pais2026valleyresolved,
title = {{Valley-resolved high harmonics probe symmetry breaking beyond the Dirac cone}},
author = {Pablo Pais and Alfredo Iorio and Marcelo F. Ciappina},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15251},
eprint = {2610.15251},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15251},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Valley-resolved high harmonics probe symmetry breaking beyond the Dirac cone
AU - Pablo Pais
AU - Alfredo Iorio
AU - Marcelo F. Ciappina
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15251
UR - https://arxiv.org/abs/2610.15251
AB - Low-energy electrons in graphene obey an emergent, rotationally invariant Dirac equation, while the honeycomb lattice enters only through higher-order, symmetry-breaking corrections, the leading one being trigonal warping. This provides a unique solid-state arena to address a cornerstone challenge in quantum gravity: how to detect ultraviolet symmetry-breaking granular corrections, suppressed by a fundamental scale, atop an emergent infrared relativistic continuum. We show that intense counter-rotating ω-2ω fields and valley-resolved high-harmonic generation (HHG) provide such a probe. Within a family of models that interpolates continuously between the isotropic Dirac cone and nearest-neighbour graphene at fixed Fermi velocity, the valley contrast of the harmonic yield vanishes identically in the symmetric theory, grows linearly with the warping coupling, and its valley-even counterpart appears only at second order, as expected from effective-field-theory power counting. The stronger the laser, the farther it drives electrons from the Dirac points, so the laser intensity plays the role of the collision energy. For the fourth harmonic, the leading warping correction alone accounts for the valley contrast of real graphene up to fundamental intensities of about 10^11 W/cm^2, below the damage threshold of monolayer graphene, whereas the fifth harmonic already reveals higher-order lattice corrections at intensities around 10^10 W/cm^2. The two harmonics, which rotate in opposite directions, are emitted by opposite valleys. Valley-resolved harmonics are far more sensitive than the residual valley populations, making them a practical detector of lattice-scale physics hidden beneath an emergent Dirac theory.
ER -