{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/distribution-of-the-order-parameter-in","title":"Distribution of the order parameter in strongly disordered superconductors: An analytic theory","arxiv_id":"2106.11848","date":"2021-06-22","proceeding":null,"authors":["Anton V. Khvalyuk","Mikhail V. Feigel'man"],"abstract":"We developed an analytic theory of inhomogeneous superconducting pairing in strongly disordered materials, which are moderately close to superconducting-insulator transition. Single-electron eigenstates are assumed to be Anderson-localized, with a large localization volume. Superconductivity develops due to coherent delocalization of originally localized pre-formed Cooper pairs. The key assumption of the theory is that each such pair is coupled to a large number $Z\\gg1$ of similar neighboring pairs. We derived integral equations for the probability distribution $P\\left(\\Delta\\right)$ of local superconducting order parameter $\\Delta\\left(\\boldsymbol{r}\\right)$ and analyzed their solutions in the limit of small dimensionless Cooper coupling constant $\\lambda\\ll1$. The shape of the order-parameter distribution is found to depend crucially upon the effective number of nearest neighbors $Z_{\\text{eff}}=2\\nu_{0}\\Delta_{0}Z$. The solution we provide is valid both at large and small $Z_{\\text{eff}}$; the latter case is nontrivial as the function $P\\left(\\Delta\\right)$ is heavily non-Gaussian. The discovery of a broad parameter range where the distribution function $P\\left(\\Delta\\right)$ is non-Gaussian but also non-critical (in the sense of SIT criticality) is one of our key findings. The analytic results are supplemented by numerical data, and good agreement between them is observed.","url_abs":"https://arxiv.org/abs/2106.11848v2","url_pdf":"https://arxiv.org/pdf/2106.11848v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"distribution-of-the-order-parameter-in","repo_url":"https://gitlab.com/AnwardoX/OP-distribution-numerics","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}