Superdiffusive two-dimensional superconductors
Abstract
We formulate a non-local, field-theoretic description of phase fluctuations and topological transitions in two-dimensional (2D) superconductors by generalizing the local only-phase Popov action to a framework utilizing non-local fractional operators. By replacing the standard spatial Laplacian with the Riesz fractional Laplacian −(−∇2)α/2 (where 1<α<2), we prove that the vortex-antivortex interaction transitions from logarithmic confinement to a stronger power-law confinement of the form V(r)∝ r2−α. Through a generalized Kosterlitz-Thouless energetic-entropic analysis, we demonstrate that this non-local confinement strictly suppresses thermal vortex proliferation. Because the non-local operator safely places the system outside the strict domain of validity of the Mermin-Wagner restriction, this power-law confinement natively stabilizes true long-range order at finite temperatures. Finally, by constructing a gauge-invariant fractional action, we formulate a fractional London equation. This approach yields a real-space power-law kernel that maps directly onto the anomalous Pippard limit of superconductors with long coherence lengths, providing a unified phenomenologically motivated framework for non-local electrodynamics.
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BibTeX
@misc{tolbatov2026superdiffusive,
title = {{Superdiffusive two-dimensional superconductors}},
author = {Iogann Tolbatov and Luca Salasnich},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05447},
eprint = {2609.05447},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05447},
}
RIS
TY - UNPB
TI - Superdiffusive two-dimensional superconductors
AU - Iogann Tolbatov
AU - Luca Salasnich
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.05447
UR - https://arxiv.org/abs/2609.05447
AB - We formulate a non-local, field-theoretic description of phase fluctuations and topological transitions in two-dimensional (2D) superconductors by generalizing the local only-phase Popov action to a framework utilizing non-local fractional operators. By replacing the standard spatial Laplacian with the Riesz fractional Laplacian −(−∇^2)^α/2 (where 1<α<2), we prove that the vortex-antivortex interaction transitions from logarithmic confinement to a stronger power-law confinement of the form V(r)∝ r^2−α. Through a generalized Kosterlitz-Thouless energetic-entropic analysis, we demonstrate that this non-local confinement strictly suppresses thermal vortex proliferation. Because the non-local operator safely places the system outside the strict domain of validity of the Mermin-Wagner restriction, this power-law confinement natively stabilizes true long-range order at finite temperatures. Finally, by constructing a gauge-invariant fractional action, we formulate a fractional London equation. This approach yields a real-space power-law kernel that maps directly onto the anomalous Pippard limit of superconductors with long coherence lengths, providing a unified phenomenologically motivated framework for non-local electrodynamics.
ER -