Chiral superconductivity on a closed Klein bottle: a chirality wall and its Majorana seam spectrum
Abstract
We study a spinless π-flux lattice superconductor whose normal-state momentum-space fundamental domain is a Klein bottle. Within this model, a glide lift and a hidden antiunitary symmetry independently force the Bogoliubov--de Gennes (BdG) Chern number to vanish. A diagonal pairing breaks the antiunitary obstruction exactly when its real part is nonzero; this is necessary, not sufficient, for a chiral phase. We derive explicit Pfaffians determining Chern parity and identify three analytic families of gap closings in a real-pairing section. For a chiral state on a closed real-space Klein bottle, the prescribed pairing and gluing produce a ΔC=2 chirality wall. A translation-invariant unfolding resolves two co-propagating Majorana branches. Their finite-size levels depend on circumference and holonomy; the near-zero pair is lifted at first order by allowed local seam perturbations. A cut-cylinder control has the same low-energy channel count, so gluing reconnects existing gapless content. We also distinguish literal gluing from deck projection: particle--hole symmetry exchanges the deck eigenblocks, precluding their interpretation as independent BdG quotient Hamiltonians. The contribution is a model-specific account of pairing compatibility and closed-surface seam spectra. The energy cost is evaluated for a fixed pairing background; neither a protected zero mode nor a self-consistent wall solution is claimed.
Related
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BibTeX
@misc{junhao2026chiral,
title = {{Chiral superconductivity on a closed Klein bottle: a chirality wall and its Majorana seam spectrum}},
author = {Junhao and Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40251},
eprint = {2610.40251},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40251},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Chiral superconductivity on a closed Klein bottle: a chirality wall and its Majorana seam spectrum
AU - Junhao
AU - Wang
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40251
UR - https://arxiv.org/abs/2610.40251
AB - We study a spinless π-flux lattice superconductor whose normal-state momentum-space fundamental domain is a Klein bottle. Within this model, a glide lift and a hidden antiunitary symmetry independently force the Bogoliubov--de Gennes (BdG) Chern number to vanish. A diagonal pairing breaks the antiunitary obstruction exactly when its real part is nonzero; this is necessary, not sufficient, for a chiral phase. We derive explicit Pfaffians determining Chern parity and identify three analytic families of gap closings in a real-pairing section. For a chiral state on a closed real-space Klein bottle, the prescribed pairing and gluing produce a ΔC=2 chirality wall. A translation-invariant unfolding resolves two co-propagating Majorana branches. Their finite-size levels depend on circumference and holonomy; the near-zero pair is lifted at first order by allowed local seam perturbations. A cut-cylinder control has the same low-energy channel count, so gluing reconnects existing gapless content. We also distinguish literal gluing from deck projection: particle--hole symmetry exchanges the deck eigenblocks, precluding their interpretation as independent BdG quotient Hamiltonians. The contribution is a model-specific account of pairing compatibility and closed-surface seam spectra. The energy cost is evaluated for a fixed pairing background; neither a protected zero mode nor a self-consistent wall solution is claimed.
ER -