Evanescent-mode Casimir-Josephson force and gate-controlled resonances in ballistic graphene Josephson junctions
Abstract
We develop a microscopic scattering theory of the phase-dependent equilibrium mechanical response of a ballistic superconductor-graphene-superconductor Josephson junction. The calculation is based on an energy-dependent Dirac scattering matrix embedded in a normalized Matsubara determinant, so the reported force correction contains the complete Bogoliubov-de Gennes spectrum of the stated ideal model. At charge neutrality the full determinant approaches a closed-form evanescent-mode result proportional to ΔW/L2, reaching 2ln 2 ΔW/(πL2) at phase difference π in the zero-temperature short-junction limit. Gate doping produces propagating channels and Fabry-Pérot structure, causing large oscillations and sign reversals of the phase-dependent force correction δF=F(ϕ)−F(0). We distinguish the interband-to-intraband Andreev crossover, controlled by |μ|/Δ, from the evanescent-to-propagating crossover, controlled by |μ|L/(ℏ vF). Exact real-energy subgap poles obtained from the same energy-dependent scattering matrix are used to diagnose specular/interband and retro/intraband character; these labels are not treated as separately measurable thermodynamic forces in the mixed regime. We also quantify the difference between the complete determinant result and the frozen-scattering short-junction approximation without identifying that difference with a pure continuum force. The resulting gate- and phase-dependent mechanical signal provides a Dirac-material extension of earlier superconductivity-induced mechanical-force proposals.
Related
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BibTeX
@misc{salim2026evanescentmode,
title = {{Evanescent-mode Casimir-Josephson force and gate-controlled resonances in ballistic graphene Josephson junctions}},
author = {Shahrukh Salim},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30438},
eprint = {2608.30438},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30438},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Evanescent-mode Casimir-Josephson force and gate-controlled resonances in ballistic graphene Josephson junctions
AU - Shahrukh Salim
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30438
UR - https://arxiv.org/abs/2608.30438
AB - We develop a microscopic scattering theory of the phase-dependent equilibrium mechanical response of a ballistic superconductor-graphene-superconductor Josephson junction. The calculation is based on an energy-dependent Dirac scattering matrix embedded in a normalized Matsubara determinant, so the reported force correction contains the complete Bogoliubov-de Gennes spectrum of the stated ideal model. At charge neutrality the full determinant approaches a closed-form evanescent-mode result proportional to ΔW/L^2, reaching 2ln 2 ΔW/(πL^2) at phase difference π in the zero-temperature short-junction limit. Gate doping produces propagating channels and Fabry-Pérot structure, causing large oscillations and sign reversals of the phase-dependent force correction δF=F(ϕ)−F(0). We distinguish the interband-to-intraband Andreev crossover, controlled by |μ|/Δ, from the evanescent-to-propagating crossover, controlled by |μ|L/(ℏ v_F). Exact real-energy subgap poles obtained from the same energy-dependent scattering matrix are used to diagnose specular/interband and retro/intraband character; these labels are not treated as separately measurable thermodynamic forces in the mixed regime. We also quantify the difference between the complete determinant result and the frozen-scattering short-junction approximation without identifying that difference with a pure continuum force. The resulting gate- and phase-dependent mechanical signal provides a Dirac-material extension of earlier superconductivity-induced mechanical-force proposals.
ER -