{
  "abstract": "In a bulk 3D type-II superconductor, the lower critical field at which an isolated vortex becomes thermodynamically favorable is a size-independent material property. We show that the situation is different in 2D superconductors: the larger the superconductor, the weaker the field needed to create its first vortex. The lower critical field in 2D is always size-dependent. For a disk of area $\\mathcal A$, the lower critical field $B_v(\\mathcal A)$ scales as $\\mathcal A^{-1}\\ln(\\mathcal A/\\mathcal A_0)$ in the weak-screening regime and as $\\mathcal A^{-1/2}$ in the strong-screening regime. We derive these results from an analytically tractable microscopic model that admits many-body wavefunctions for both the uniform and singly quantized vortex states in a magnetic field, and incorporate screening by coupling their long-distance 2D supercurrents to 3D Maxwell equations. These results motivate organizing the weak-field ground-state of a 2D superconductor in the $(1/\\mathcal A,B)$ plane. The origin represents the zero-field thermodynamic limit and it is singular. Approaching the origin along the $B$ axis leads to an increasingly dilute vortex lattice, whereas approaching along the $1/\\mathcal A$ axis yields the uniform vortex-free state. Our theory shows that every trajectory carrying fixed finite flux ultimately approaches the vortex-free state in the thermodynamic limit and provides a firm microscopic foundation for the weak-field thermodynamics of 2D superconductors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01602",
  "author_total": 2,
  "authors": [
    {
      "name": "Guopeng Xu"
    },
    {
      "name": "Chunli Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8f8496s0w6wsf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01602",
  "fulltext_url": null,
  "id": "8f8496s0w6wsf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01602",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mes-hall"
    ],
    [
      "arxiv",
      "cond-mat.supr-con"
    ],
    [
      "openalex",
      "3104|Physics of Superconductivity and Magnetism"
    ]
  ],
  "openalex": "W7206181736",
  "pdf_url": "https://arxiv.org/pdf/2609.01602",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8f8496s0w6wsf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "2609.01602",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01602"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Singular Weak-Field Thermodynamics of 2D Superconductors",
  "title_text": "Singular Weak-Field Thermodynamics of 2D Superconductors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:00Z",
  "url": "https://research.draconitic.com/paper/8f8496s0w6wsf",
  "venue": "arXiv",
  "versions": []
}