Vortex-core Majorana coupling to a chiral edge in a px+ipy superconductor: Nonmonotonic spectral reorganization and coherent fermion-parity dynamics
Abstract
We study how vortex--edge coupling reorganizes the low-energy sector of a finite two-dimensional px+ipy superconducting disk as a function of the vortex--boundary separation d and examine what this reorganization implies for the parity memory associated with a prescribed vortex-core Majorana wave packet, a resource relevant to Majorana-based quantum operations. Bogoliubov--de Gennes calculations reveal nonmonotonic core--edge reorganization of the lowest positive-energy finite-disk eigenstate, with particularly rapid variation near d≃7ξ, where ξ is the coherence length. To separate this eigenstate reorganization from the spectral representation of a prescribed state, we rigidly translate a centered-vortex core-reference packet to each fixed vortex position, restrict it to the target disk, and project it, without intermediate normalization, onto the particle-hole-complete low-energy subspace. For Δ0/EF=0.36 and disk radius R=30ξ, the resulting retained norm exceeds 0.98 at all six sampled separations, 4.25≤ d/ξ≤8.25, while, depending on d, the spectral measure is concentrated near zero energy, fragmented over several low-energy levels, or dominated by finite-energy weight. Correspondingly, the signed parity correlator displays slow temporal variation, rapid coherent dephasing, or sign-changing oscillations, with possible finite-size recurrences at later times. Thus a large retained norm does not by itself imply spectral concentration or persistent parity memory.
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BibTeX
@misc{liu2026vortexcore,
title = {{Vortex-core Majorana coupling to a chiral edge in a $p_x+ip_y$ superconductor: Nonmonotonic spectral reorganization and coherent fermion-parity dynamics}},
author = {Peiyao Liu and Yi Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02260},
eprint = {2609.02260},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02260},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Vortex-core Majorana coupling to a chiral edge in a p_x+ip_y superconductor: Nonmonotonic spectral reorganization and coherent fermion-parity dynamics
AU - Peiyao Liu
AU - Yi Zhou
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02260
UR - https://arxiv.org/abs/2609.02260
AB - We study how vortex--edge coupling reorganizes the low-energy sector of a finite two-dimensional p_x+ip_y superconducting disk as a function of the vortex--boundary separation d and examine what this reorganization implies for the parity memory associated with a prescribed vortex-core Majorana wave packet, a resource relevant to Majorana-based quantum operations. Bogoliubov--de Gennes calculations reveal nonmonotonic core--edge reorganization of the lowest positive-energy finite-disk eigenstate, with particularly rapid variation near d≃7ξ, where ξ is the coherence length. To separate this eigenstate reorganization from the spectral representation of a prescribed state, we rigidly translate a centered-vortex core-reference packet to each fixed vortex position, restrict it to the target disk, and project it, without intermediate normalization, onto the particle-hole-complete low-energy subspace. For Δ_0/E_F=0.36 and disk radius R=30ξ, the resulting retained norm exceeds 0.98 at all six sampled separations, 4.25≤ d/ξ≤8.25, while, depending on d, the spectral measure is concentrated near zero energy, fragmented over several low-energy levels, or dominated by finite-energy weight. Correspondingly, the signed parity correlator displays slow temporal variation, rapid coherent dephasing, or sign-changing oscillations, with possible finite-size recurrences at later times. Thus a large retained norm does not by itself imply spectral concentration or persistent parity memory.
ER -