Weak-Coupling Pair-Density-Wave from Momentum-Space Nonsymmorphic Symmetry

@misc{li2026weakcoupling,
  title = {{Weak-Coupling Pair-Density-Wave from Momentum-Space Nonsymmorphic Symmetry}},
  author = {Ming-Rui Li and Zhengzhi Wu and Hong Yao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28630},
  eprint = {2609.28630},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28630},
}

TY  - UNPB
TI  - Weak-Coupling Pair-Density-Wave from Momentum-Space Nonsymmorphic Symmetry
AU  - Ming-Rui Li
AU  - Zhengzhi Wu
AU  - Hong Yao
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28630
UR  - https://arxiv.org/abs/2609.28630
AB  - Pair-density-wave (PDW) order is a superconducting state with a spatially modulated order parameter and is generally subleading to uniform superconductivity within the conventional weak-coupling BCS paradigm. Here, using a twisted bilayer checkerboard-lattice model, we show that momentum-space nonsymmorphic symmetry provides a generic mechanism that can instead promote PDW order to a leading weak-coupling instability. Combining a controlled Wilsonian renormalization-group analysis at charge neutrality with a finite-doping Bethe--Salpeter analysis, we determine the leading ordering tendencies among various competing instabilities. At charge neutrality, two symmetry-related quadratic band touchings support spin-singlet and spin-triplet PDW instabilities for different attractive interactions, whereas repulsive interactions favor quantum Hall insulators and finite-Q density-wave orders. Upon doping, the nonsymmorphic symmetry, together with time reversal, protects the Cooper logarithm in the finite-momentum Q pairing channel at generic fillings, allowing PDW order to remain a leading instability over the broad doping range studied. This mechanism extends naturally to moiré Chern bands: by breaking time-reversal symmetry while preserving the nonsymmorphic symmetry and inversion, we obtain a fully gapped topological spin-triplet PDW state with BdG Chern number C_BdG=8. Our results establish momentum-space nonsymmorphic symmetry as a general weak-coupling route to PDW superconductivity, including topological PDW states.
ER  -