Quantum Geometric Origin of Yu-Shiba-Rusinov States
Abstract
In this work, we revisit the classic Yu-Shiba-Rusinov (YSR) problem of magnetic impurities in s-wave superconductors and uncover a quantum geometric origin of the YSR bound-state structure. The key geometric quantity is the momentum-space average of Bloch band projector over low-energy electrons, whose matrix rank, positive eigenvalues, and corresponding eigenvectors directly control the number, energies, and symmetry representations of the YSR states, respectively. As a result, a superconductor with nontrivial normal-state quantum geometry can host more bound states than its trivial counterpart, even if they share the same electronic dispersion. We apply our theory to monolayer 1H-NbSe2 and find that the geometric texture of its single superconducting band enforces three symmetry-distinct YSR channels for a magnetic point impurity at Nb or Se sites. Our work opens a route to probing normal-state wavefunction geometry through local YSR spectroscopy.
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BibTeX
@misc{zhang2026quantum,
title = {{Quantum Geometric Origin of Yu-Shiba-Rusinov States}},
author = {Rui-Xing Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31920},
eprint = {2609.31920},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31920},
}
RIS
TY - UNPB
TI - Quantum Geometric Origin of Yu-Shiba-Rusinov States
AU - Rui-Xing Zhang
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31920
UR - https://arxiv.org/abs/2609.31920
AB - In this work, we revisit the classic Yu-Shiba-Rusinov (YSR) problem of magnetic impurities in s-wave superconductors and uncover a quantum geometric origin of the YSR bound-state structure. The key geometric quantity is the momentum-space average of Bloch band projector over low-energy electrons, whose matrix rank, positive eigenvalues, and corresponding eigenvectors directly control the number, energies, and symmetry representations of the YSR states, respectively. As a result, a superconductor with nontrivial normal-state quantum geometry can host more bound states than its trivial counterpart, even if they share the same electronic dispersion. We apply our theory to monolayer 1H-NbSe_2 and find that the geometric texture of its single superconducting band enforces three symmetry-distinct YSR channels for a magnetic point impurity at Nb or Se sites. Our work opens a route to probing normal-state wavefunction geometry through local YSR spectroscopy.
ER -