Stimulation of superconductivity in d-wave superconductors
Abstract
We study the stimulation of superconductivity by an external electromagnetic radiation --- the Eliashberg effect --- in a disordered d-wave superconductor. We use the self-consistent Keldysh--Nambu quasiclassical formalism augmented by an inelastic relaxation term to compute the static correction to the pairing amplitude by treating elastic scattering within the Born approximation with the full second-order impurity vertex retained. We find that the clean d-wave superconductor shows no enhancement at any frequency: without a momentum relaxation channel a spatially uniform drive produces no absorption, only pair breaking. Elastic impurity scattering restores absorption and with it activates response in the Eliashberg channel. We find enhancement of the pairing amplitude which is confined to a bounded window in frequency, disorder strength, inelastic scattering rate and gap magnitude. Both edges of the window scale with the gap but are set by the competition between quasiparticle redistribution, heating and pair breaking rather than by a feature of the spectrum. Furthermore, in contrast to the s-wave when the threshold is pinned at 2Δ, the upper edge is not pinned to the maximum gap and crosses it as the system approaches the critical temperature.
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BibTeX
@misc{steineman2026stimulation,
title = {{Stimulation of superconductivity in $d$-wave superconductors}},
author = {Aidan Steineman and Maxim Dzero},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28624},
eprint = {2609.28624},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28624},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Stimulation of superconductivity in d-wave superconductors
AU - Aidan Steineman
AU - Maxim Dzero
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28624
UR - https://arxiv.org/abs/2609.28624
AB - We study the stimulation of superconductivity by an external electromagnetic radiation --- the Eliashberg effect --- in a disordered d-wave superconductor. We use the self-consistent Keldysh--Nambu quasiclassical formalism augmented by an inelastic relaxation term to compute the static correction to the pairing amplitude by treating elastic scattering within the Born approximation with the full second-order impurity vertex retained. We find that the clean d-wave superconductor shows no enhancement at any frequency: without a momentum relaxation channel a spatially uniform drive produces no absorption, only pair breaking. Elastic impurity scattering restores absorption and with it activates response in the Eliashberg channel. We find enhancement of the pairing amplitude which is confined to a bounded window in frequency, disorder strength, inelastic scattering rate and gap magnitude. Both edges of the window scale with the gap but are set by the competition between quasiparticle redistribution, heating and pair breaking rather than by a feature of the spectrum. Furthermore, in contrast to the s-wave when the threshold is pinned at 2Δ, the upper edge is not pinned to the maximum gap and crosses it as the system approaches the critical temperature.
ER -