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First-Principles Calculation of Coherence Length and Penetration Depth Based on Density Functional Theory for Superconductors

Mitsuaki Kawamura1,*, Takuya Nomoto2, Niklas Witt3,4, and Ryotaro Arita5,6

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Phys. Rev. Lett. 137, 196001 – Published 3 November, 2026

DOI: https://doi.org/10.1103/lrhl-j9bt

Abstract

We develop a first-principles framework for evaluating the fundamental length scales of superconductivity, namely the coherence length ξ0 and the magnetic penetration depth λL, within superconducting density functional theory. By incorporating finite-momentum Cooper pairs, we formulate a microscopic scheme that enables a consistent and parameter-free determination of ξ0, λL, and the superconducting transition temperature Tc on the same theoretical footing. Applying the method to representative elemental superconductors, the A15 compound V3Si, and H3S under high pressure, we obtain results in good agreement with available experimental data and reproduce the type-I or type-II classification across all materials studied. The unified access to ξ0 and λL further allows us to construct the Uemura plot entirely from first principles, showing that higher-Tc systems are characterized by the simultaneous realization of strong pairing and large phase stiffness. Our results establish a predictive first-principles route to superconducting length scales and provide a microscopic interpretation of empirical correlations in superconductivity.

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synopsis

Calculating Superconductors from Scratch

Published 3 November, 2026

A new formalism yields the quantities that characterize a conventional superconductor without adjustable parameters.

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Phys. Rev. Lett. 137, 196001– Published 3 November, 2026
  • Received 9 March 2026
  • Revised 6 August 2026
  • Accepted 1 September 2026
Article part of CHORUS
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