{
  "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.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Physics and Astronomy, University of Notre Dame, Notre Dame, IN 46556",
    "Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, IN 46556"
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Xiaoyu Ma"
    },
    {
      "affs": [
        0
      ],
      "name": "Wenzhao Li",
      "orcid": "0000-0003-1112-8336"
    },
    {
      "affs": [
        0
      ],
      "name": "Dipanjan Ray",
      "orcid": "0009-0000-1272-0070"
    },
    {
      "affs": [
        0
      ],
      "name": "Zoltán Toroczkai",
      "orcid": "0000-0002-6602-2849"
    },
    {
      "affs": [
        0,
        1
      ],
      "name": "Boldizsár Jankó",
      "orcid": "0000-0002-1744-3348"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3prt5s50dwg0p.bib",
  "cited_by": 0,
  "doi": "10.1073/pnas.2602186123",
  "fulltext_url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC13732197/",
  "id": "3prt5s50dwg0p",
  "issns": [
    "0027-8424",
    "1091-6490"
  ],
  "landing_url": "https://doi.org/10.1073/pnas.2602186123",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "heading",
      "426"
    ],
    [
      "heading",
      "Physical Sciences"
    ],
    [
      "heading",
      "Physics"
    ],
    [
      "openalex",
      "3104|Physics of Superconductivity and Magnetism"
    ]
  ],
  "openalex": "W7221948583",
  "pdf_url": null,
  "pmcid": "PMC13732197",
  "pmid": "42956028",
  "published": "2026-10-29",
  "publisher": "National Academy of Sciences",
  "ris": "https://research.draconitic.com/paper/3prt5s50dwg0p.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:22:13Z",
      "native_id": "PMC13732197",
      "source": "pmc",
      "url": "https://doi.org/10.1073/pnas.2602186123"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3104|Physics of Superconductivity and Magnetism",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Potential energy landscape networks of confined vortex matter",
  "title_text": "Potential energy landscape networks of confined vortex matter",
  "type": "peer-reviewed",
  "updated_at": "2026-11-08T12:22:13Z",
  "url": "https://research.draconitic.com/paper/3prt5s50dwg0p",
  "venue": "Proceedings of the National Academy of Sciences of the United States of America",
  "versions": []
}