Collective phase modes in twisted d-wave superconducting bilayers
Abstract
Twisted cuprate bilayers have been predicted to host high-temperature chiral d+id' superconductivity, originating from higher-order Josephson coupling processes. In such two-dimensional superconducting systems, long-wavelength fluctuations in the phase of the superconducting order parameter constitute gapless collective modes and therefore remain significant even at zero temperature. Here, we perform a theoretical analysis of the low-energy phase fluctuations in twisted d-wave superconducting bilayers within a self-consistent harmonic approximation, systematically retaining Josephson coupling to all orders. We demonstrate that higher-order Josephson coupling processes lead to nontrivial modifications of the phase dynamics. The momentum-resolved summand of the relative-phase stiffness is nonzero even in the normal state because interlayer tunneling explicitly breaks the intralayer U(1) symmetry, but its momentum integral vanishes for the continuum dispersion. The relative-phase stiffness is smaller in the d+id' phase than in the d-wave phase, while the overall-phase stiffness has the opposite behavior. Furthermore, phase fluctuations strongly soften the Josephson plasma frequency near a twist angle of 45∘ and also substantially reduce the Josephson critical current.
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BibTeX
@misc{shi2026collective,
title = {{Collective phase modes in twisted $d$-wave superconducting bilayers}},
author = {Yin Shi and Mengxian Zhao and Fei Yang and Miao Liu and Sheng Meng},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.00662},
eprint = {2607.00662},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.00662},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Collective phase modes in twisted d-wave superconducting bilayers
AU - Yin Shi
AU - Mengxian Zhao
AU - Fei Yang
AU - Miao Liu
AU - Sheng Meng
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2607.00662
UR - https://arxiv.org/abs/2607.00662
AB - Twisted cuprate bilayers have been predicted to host high-temperature chiral d+id' superconductivity, originating from higher-order Josephson coupling processes. In such two-dimensional superconducting systems, long-wavelength fluctuations in the phase of the superconducting order parameter constitute gapless collective modes and therefore remain significant even at zero temperature. Here, we perform a theoretical analysis of the low-energy phase fluctuations in twisted d-wave superconducting bilayers within a self-consistent harmonic approximation, systematically retaining Josephson coupling to all orders. We demonstrate that higher-order Josephson coupling processes lead to nontrivial modifications of the phase dynamics. The momentum-resolved summand of the relative-phase stiffness is nonzero even in the normal state because interlayer tunneling explicitly breaks the intralayer U(1) symmetry, but its momentum integral vanishes for the continuum dispersion. The relative-phase stiffness is smaller in the d+id' phase than in the d-wave phase, while the overall-phase stiffness has the opposite behavior. Furthermore, phase fluctuations strongly soften the Josephson plasma frequency near a twist angle of 45^∘ and also substantially reduce the Josephson critical current.
ER -