Singular Weak-Field Thermodynamics of 2D Superconductors
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 π, the lower critical field Bv(π) scales as πβ1ln(π/π0) in the weak-screening regime and as πβ1/2 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/π,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/π 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.
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BibTeX
@misc{xu2026singular,
title = {{Singular Weak-Field Thermodynamics of 2D Superconductors}},
author = {Guopeng Xu and Chunli Huang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01602},
eprint = {2609.01602},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01602},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Singular Weak-Field Thermodynamics of 2D Superconductors
AU - Guopeng Xu
AU - Chunli Huang
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01602
UR - https://arxiv.org/abs/2609.01602
AB - 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 π, the lower critical field B_v(π) scales as π^β1ln(π/π_0) in the weak-screening regime and as π^β1/2 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/π,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/π 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.
ER -