Two superconducting pairing models with a Kitaev spin-liquid glue: microscopic kernel and parity alternation on odd-fold bond stars
Abstract
We construct two superconducting pairing models on doped Kitaev honeycomb, whose microscopic kernels are derived rather than assumed. Both are driven by a bond-local glue neutral between the even- and odd-parity pairing channels; the chirality--parity linkage is set by bond-star geometry, not by the microscopic glue. (i) Model~1(odd-parity sector): the kernel follows from the flux-sector selection rule of the pure model, fixing its component-diagonal, nearest-neighbor separable, rank-one-per-bond form, with wα=JK2χα∝ rαmα, where mα follows from the Hellmann--Feynman theorem and rα≃0.24 is computed numerically. The spin-vertex state is a unitary triplet with a bond-locked anisotropic d vector; its gap is a Gram sum of bond sines, so nodal directions are fixed by geometry. (ii) Model~2(even): the kernel is fixed by the C3 little-group selection rule of a zone-corner chiral phonon, up to a Cooper-channel extension whose momentum constraint we state explicitly. The charge-vertex pairing is a d+id singlet: the parity decomposition f±=g±+p± projects onto g±, so chirality is slaved to the phonon polarization, with C=±4 and κxy/T=2κ0. Reversing the pump helicity reverses the Chern number, Kerr rotation, and thermal Hall sign. (iii) General theorem: on odd-fold bond stars, the angular-momentum ladder of a single-star chiral form factor alternates in parity. Every chiral state selected by such a bond-local form factor is a geometrically enforced singlet--triplet composite with universal amplitude ratios (n=3: d⊕ p; n=5: g⊕ p or d⊕ f); coherent doubled-star combinations can restore parity purity. The Chern number of the mixed state follows the dominant on-shell component across a topological boundary. The spin glue drives C=±2; the charge kernel C=±4.
Related
- Kitaev spin liquid in superconducting networks
- Dynamical quantum phase transitions in a pseudo-Hermitian Hamiltonian: The imbalanced-pairing Kitaev model
- Modeling Logical Gates and Readout of Superconducting Gottesman-Kitaev-Preskill Qubits
- Kibble--Zurek Mechanism and Defect Freezing in Imbalanced-Pairing Kitaev Models
- Slave-boson Formalism for Superconducting Pairing at Strong Coupling
BibTeX
@misc{dai2026superconducting,
title = {{Two superconducting pairing models with a Kitaev spin-liquid glue: microscopic kernel and parity alternation on odd-fold bond stars}},
author = {Youping Dai},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06157},
eprint = {2610.06157},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06157},
}
RIS
TY - UNPB
TI - Two superconducting pairing models with a Kitaev spin-liquid glue: microscopic kernel and parity alternation on odd-fold bond stars
AU - Youping Dai
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06157
UR - https://arxiv.org/abs/2610.06157
AB - We construct two superconducting pairing models on doped Kitaev honeycomb, whose microscopic kernels are derived rather than assumed. Both are driven by a bond-local glue neutral between the even- and odd-parity pairing channels; the chirality--parity linkage is set by bond-star geometry, not by the microscopic glue. (i) Model~1(odd-parity sector): the kernel follows from the flux-sector selection rule of the pure model, fixing its component-diagonal, nearest-neighbor separable, rank-one-per-bond form, with w_α=J_K^2χ_α∝ r_αm_α, where m_α follows from the Hellmann--Feynman theorem and r_α≃0.24 is computed numerically. The spin-vertex state is a unitary triplet with a bond-locked anisotropic d vector; its gap is a Gram sum of bond sines, so nodal directions are fixed by geometry. (ii) Model~2(even): the kernel is fixed by the C_3 little-group selection rule of a zone-corner chiral phonon, up to a Cooper-channel extension whose momentum constraint we state explicitly. The charge-vertex pairing is a d+id singlet: the parity decomposition f_±=g_±+p_± projects onto g_±, so chirality is slaved to the phonon polarization, with C=±4 and κ_xy/T=2κ_0. Reversing the pump helicity reverses the Chern number, Kerr rotation, and thermal Hall sign. (iii) General theorem: on odd-fold bond stars, the angular-momentum ladder of a single-star chiral form factor alternates in parity. Every chiral state selected by such a bond-local form factor is a geometrically enforced singlet--triplet composite with universal amplitude ratios (n=3: d⊕ p; n=5: g⊕ p or d⊕ f); coherent doubled-star combinations can restore parity purity. The Chern number of the mixed state follows the dominant on-shell component across a topological boundary. The spin glue drives C=±2; the charge kernel C=±4.
ER -