Symmetry-selected extreme shear compliance in a stable carbon monolayer
Abstract
Extreme stiffness contrasts between loading modes usually require architected metamaterials with compliant hinges, whereas covalent crystals rarely exhibit such behavior intrinsically. Here, density functional theory calculations of the complete in-plane elastic tensors of four tetragonal carbon monolayers reveal a more than 50-fold spread in shear stiffness, despite less than a twofold variation in axial stiffness and the same symmetry-allowed tensor form. Twin T-graphene shows the strongest contrast: its shear constant, C66=3.03~N m−1, is 47 times smaller than in graphene and yields a shear Kelvin eigenvalue 29 times below the two normal-strain eigenvalues, while the Born stability criteria hold. This shear constant revises an earlier inference of elastic isotropy based on normal strains alone. Constrained relaxations and symmetry-resolved mode analysis identify the mechanism as a B2g counter-torsion of the carbon sublayers about the mid-plane bonds, which removes 96.3% of the clamped-ion shear stiffness with bond-length changes below 0.15%. An internal-coordinate model quantifies this cancellation, identifying internal relaxation, rather than weak bonding, as the origin of the soft channel. The resulting anisotropy predicts transverse sound velocities of 1.95 km s−1 along [100] and 10.62 km s−1 along [110], a testable acoustic signature. Phonon calculations, ab initio molecular dynamics at 300 K, and large-deformation simulations indicate that the soft channel is dynamically stable, preserves the local bonding, and persists beyond the harmonic regime. Our results show how bonding topology enables extreme mode-selective elasticity through internal relaxation in a mechanically stable covalent crystal.
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BibTeX
@misc{gonzalez2026symmetryselected,
title = {{Symmetry-selected extreme shear compliance in a stable carbon monolayer}},
author = {J. W. González and M. Pacheco and J. D. Correa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19168},
eprint = {2610.19168},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19168},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Symmetry-selected extreme shear compliance in a stable carbon monolayer
AU - J. W. González
AU - M. Pacheco
AU - J. D. Correa
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.19168
UR - https://arxiv.org/abs/2610.19168
AB - Extreme stiffness contrasts between loading modes usually require architected metamaterials with compliant hinges, whereas covalent crystals rarely exhibit such behavior intrinsically. Here, density functional theory calculations of the complete in-plane elastic tensors of four tetragonal carbon monolayers reveal a more than 50-fold spread in shear stiffness, despite less than a twofold variation in axial stiffness and the same symmetry-allowed tensor form. Twin T-graphene shows the strongest contrast: its shear constant, C_66=3.03~N m^−1, is 47 times smaller than in graphene and yields a shear Kelvin eigenvalue 29 times below the two normal-strain eigenvalues, while the Born stability criteria hold. This shear constant revises an earlier inference of elastic isotropy based on normal strains alone. Constrained relaxations and symmetry-resolved mode analysis identify the mechanism as a B_2g counter-torsion of the carbon sublayers about the mid-plane bonds, which removes 96.3% of the clamped-ion shear stiffness with bond-length changes below 0.15%. An internal-coordinate model quantifies this cancellation, identifying internal relaxation, rather than weak bonding, as the origin of the soft channel. The resulting anisotropy predicts transverse sound velocities of 1.95 km s^−1 along [100] and 10.62 km s^−1 along [110], a testable acoustic signature. Phonon calculations, ab initio molecular dynamics at 300 K, and large-deformation simulations indicate that the soft channel is dynamically stable, preserves the local bonding, and persists beyond the harmonic regime. Our results show how bonding topology enables extreme mode-selective elasticity through internal relaxation in a mechanically stable covalent crystal.
ER -