Impurity-dependent quantum geometry in 2D flat band superconductors
Abstract
In flat band superconductors, quantum geometry, rather than kinetic energy, governs pairing and transport. However, how this geometry manifests in the response to a local, individually addressable impurity remains largely unexplored. Here, we study the Yu-Shiba-Rusinov (YSR) bound state induced by a magnetic adatom that hybridizes with every orbital of a two-dimensional flat band superconductor, and characterize its spatial profile using two quantities: the quadratic spread QS and the localization length ξ. We show that QS is not set by the quantum metric alone, as geometric corrections arising from inter-orbital interference and, more importantly, from the anisotropy of the adatom-lattice hybridization contribute on equal footing, making QS strongly impurity dependent and tunable. On the other hand, ξ emerges from the projection onto the flat band alone and is a universal property set by the overlap of compact localized states. All impurity dependence is instead isolated in the prefactor of the wavefunction whose magnitude correlates directly with QS. We, therefore, report a clean separation between universal and impurity-tunable physics from the induced YSR bound state in these systems, and confirm our results numerically via exact diagonalization.
Related
- Quantum geometry of collective pairing fluctuations in the superfluid weight of multiband superconductors
- Nonreciprocal impurity scattering as a probe for pairing symmetries in kagome superconductors
- Flat-band quantum geometry from embedded quench dynamics
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- Orbital magnetic susceptibility and de Haas-van Alphen effect of a flat band from quantum geometry
BibTeX
@misc{cardoso2026impuritydependent,
title = {{Impurity-dependent quantum geometry in 2D flat band superconductors}},
author = {Simão S. Cardoso and Andrej Mesaros and Pascal Simon},
howpublished = {HAL},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2609.00338},
eprint = {2609.00338},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05771718v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Impurity-dependent quantum geometry in 2D flat band superconductors
AU - Simão S. Cardoso
AU - Andrej Mesaros
AU - Pascal Simon
PY - 2026
DA - 2026/08/31
PB - HAL
DO - 10.48550/arxiv.2609.00338
UR - https://hal.science/hal-05771718v1
AB - In flat band superconductors, quantum geometry, rather than kinetic energy, governs pairing and transport. However, how this geometry manifests in the response to a local, individually addressable impurity remains largely unexplored. Here, we study the Yu-Shiba-Rusinov (YSR) bound state induced by a magnetic adatom that hybridizes with every orbital of a two-dimensional flat band superconductor, and characterize its spatial profile using two quantities: the quadratic spread QS and the localization length ξ. We show that QS is not set by the quantum metric alone, as geometric corrections arising from inter-orbital interference and, more importantly, from the anisotropy of the adatom-lattice hybridization contribute on equal footing, making QS strongly impurity dependent and tunable. On the other hand, ξ emerges from the projection onto the flat band alone and is a universal property set by the overlap of compact localized states. All impurity dependence is instead isolated in the prefactor of the wavefunction whose magnitude correlates directly with QS. We, therefore, report a clean separation between universal and impurity-tunable physics from the induced YSR bound state in these systems, and confirm our results numerically via exact diagonalization.
ER -