Potential energy landscape networks of confined vortex matter
- 1Department of Physics and Astronomy, University of Notre Dame, Notre Dame, IN 46556
- 2Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, IN 46556
Abstract
Advances in nanoscale patterning of superconducting films [Y. L. Wang et al., Nat. Nanotechnol. 13, 560–565 (2018)] and the availability of submicron-sized superconducting single crystals with controlled geometry allow for the investigation of superconducting vortex matter under extreme confinement [A. K. Geim et al., Nature 390, 259–262 (1997)]. It has been observed in these systems that the interplay between sample geometry and vortex number results in the emergence of so-called “magic number” configurations which show unusually high stability against thermal fluctuations. However, a detailed, comprehensive theoretical study of the ground state and metastable states of confined vortex matter has not yet been developed. Here we show that the intricate properties of a system of vortices under extreme confinement can be characterized in detail by mapping the potential energy landscape of the system onto a network [J. P. K. Doye, Phys. Rev. Lett. 88, 238701 (2002)] with nodes corresponding to local potential energy minima and edges to transition states between local minima. We apply these techniques to systems featuring repelling particles/vortices confined in small containers of various geometric shapes. We demonstrate that the ground state almost always belongs to a subset of system states within the deepest network core. We find that the emergence of magic number configurations in the ground state results in a drastic decrease in the complexity of the entire network. We use large-scale molecular dynamics simulations to study the size dependence of melting in different configurations. We find that as confinement effects increase, magic number configurations transition to states with lower symmetry.
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BibTeX
@article{ma2026potential,
title = {{Potential energy landscape networks of confined vortex matter}},
author = {Xiaoyu Ma and Wenzhao Li and Dipanjan Ray and Zoltán Toroczkai and Boldizsár Jankó},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
year = {2026},
month = oct,
doi = {10.1073/pnas.2602186123},
url = {https://doi.org/10.1073/pnas.2602186123},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - JOUR
TI - Potential energy landscape networks of confined vortex matter
AU - Xiaoyu Ma
AU - Wenzhao Li
AU - Dipanjan Ray
AU - Zoltán Toroczkai
AU - Boldizsár Jankó
PY - 2026
DA - 2026/10/29
JO - Proceedings of the National Academy of Sciences of the United States of America
DO - 10.1073/pnas.2602186123
UR - https://doi.org/10.1073/pnas.2602186123
AB - Advances in nanoscale patterning of superconducting films [Y. L. Wang et al., Nat. Nanotechnol. 13, 560–565 (2018)] and the availability of submicron-sized superconducting single crystals with controlled geometry allow for the investigation of superconducting vortex matter under extreme confinement [A. K. Geim et al., Nature 390, 259–262 (1997)]. It has been observed in these systems that the interplay between sample geometry and vortex number results in the emergence of so-called “magic number” configurations which show unusually high stability against thermal fluctuations. However, a detailed, comprehensive theoretical study of the ground state and metastable states of confined vortex matter has not yet been developed. Here we show that the intricate properties of a system of vortices under extreme confinement can be characterized in detail by mapping the potential energy landscape of the system onto a network [J. P. K. Doye, Phys. Rev. Lett. 88, 238701 (2002)] with nodes corresponding to local potential energy minima and edges to transition states between local minima. We apply these techniques to systems featuring repelling particles/vortices confined in small containers of various geometric shapes. We demonstrate that the ground state almost always belongs to a subset of system states within the deepest network core. We find that the emergence of magic number configurations in the ground state results in a drastic decrease in the complexity of the entire network. We use large-scale molecular dynamics simulations to study the size dependence of melting in different configurations. We find that as confinement effects increase, magic number configurations transition to states with lower symmetry.
SN - 0027-8424
SN - 1091-6490
ER -