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<p>The Clinton density matrix framework of quantum crystallography is extended to superconducting systems by formulating the Kohn–Sham–Bogoliubov–de Gennes (KS-BdG) equations in a two‑component Nambu representation. In this setting, the superconducting one‑body density matrix is an idempotent projector whose normal (ρ) and anomalous (χ) blocks are determined directly from experiment: X‑ray structure factors constrain ρ while phase‑sensitive Josephson measurements constrain χ. We derive iterative Nambu–Clinton equations that enforce both sets of constraints simultaneously, thereby reconstructing the superconducting projector at T = 0 without solving directly the KS-BdG eigen value problem. This provides a rigorous, experimentally grounded route to ‘quantum crystallography’ of Cooper pairing, enabling spatial maps of |χ(r, r)|² with resolution commensurate with crystallographic data.</p>

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Superconducting quantum crystallography

  • 期刊论文

  • 发表日期：

    2025年11月13日

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  • Lou Massa

摘要

The Clinton density matrix framework of quantum crystallography is extended to superconducting systems by formulating the Kohn–Sham–Bogoliubov–de Gennes (KS-BdG) equations in a two‑component Nambu representation. In this setting, the superconducting one‑body density matrix is an idempotent projector whose normal (ρ) and anomalous (χ) blocks are determined directly from experiment: X‑ray structure factors constrain ρ while phase‑sensitive Josephson measurements constrain χ. We derive iterative Nambu–Clinton equations that enforce both sets of constraints simultaneously, thereby reconstructing the superconducting projector at T = 0 without solving directly the KS-BdG eigen value problem. This provides a rigorous, experimentally grounded route to ‘quantum crystallography’ of Cooper pairing, enabling spatial maps of |χ(r, r)|² with resolution commensurate with crystallographic data.