A First-Order Phase Transition in Spin-Imbalanced BCS Theory of Superconductivity
Abstract
We study a translation-invariant BCS functional of superconductivity for a system of spin-1/2 fermions with spin-dependent chemical potentials, μ+≠μ-. Numerical work of Caldas and Mota and analytical work of Freiji, Hainzl, and Seiringer has suggested an unusual first-order phase transition in spin-imbalanced BCS models, in which the normal state becomes globally unstable while remaining locally stable. Here, we prove that a first-order phase transition occurs in such spin-imbalanced BCS functionals. For each sufficiently small fixed spin imbalance and sufficiently low temperature, there is a coexistence coupling λfo strictly below the linear-stability threshold λlin of the normal state at which the Cooper pair density exhibits a nonzero jump and the minimized energy has a kink. The methodological insight is a coercivity estimate obtained by decomposing the BCS energy minimization into two parts, where the ``inner'' problem minimizes over the one-particle density matrices at fixed pairing and can be exactly solved by a Legendre--Fenchel transform.
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BibTeX
@misc{lemm2026firstorder,
title = {{A First-Order Phase Transition in Spin-Imbalanced BCS Theory of Superconductivity}},
author = {Marius Lemm and Barbara Roos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38961},
eprint = {2610.38961},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38961},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A First-Order Phase Transition in Spin-Imbalanced BCS Theory of Superconductivity
AU - Marius Lemm
AU - Barbara Roos
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38961
UR - https://arxiv.org/abs/2610.38961
AB - We study a translation-invariant BCS functional of superconductivity for a system of spin-1/2 fermions with spin-dependent chemical potentials, μ_+≠μ_-. Numerical work of Caldas and Mota and analytical work of Freiji, Hainzl, and Seiringer has suggested an unusual first-order phase transition in spin-imbalanced BCS models, in which the normal state becomes globally unstable while remaining locally stable. Here, we prove that a first-order phase transition occurs in such spin-imbalanced BCS functionals. For each sufficiently small fixed spin imbalance and sufficiently low temperature, there is a coexistence coupling λ_fo strictly below the linear-stability threshold λ_lin of the normal state at which the Cooper pair density exhibits a nonzero jump and the minimized energy has a kink. The methodological insight is a coercivity estimate obtained by decomposing the BCS energy minimization into two parts, where the ``inner'' problem minimizes over the one-particle density matrices at fixed pairing and can be exactly solved by a Legendre--Fenchel transform.
ER -