Electron-Phonon Coupling and Eliashberg Theory L1-325

Quantum MechanicsPhonon-mediated superconductivityδ=10 · hardL_DAG = 3.9📋 Stub — not mineable

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Unclaimed Principle — open for contribution

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Forward model E

S i g m a_{e p h} (k, o m e g a) = in t e g r a l g^{2} \cdot F (o m e g a^{'}) G (k, o m e g a - o m e g a^{'}) d o m e g a^{'}; T_{c} = (o m e g a_{l} n /1.2) \cdot e x p (- 1.04 \cdot (1 + λ) / (λ - m u \cdot - 0.62 \cdot m u \cdot λ))

Electron-phonon coupling g_{k,k'}(q,s); Eliashberg alpha^2 F(omega); BCS-like T_c from McMillan formula.

L-DAG

E.phonon_dispersion -> E.electron_phonon -> O.composite_method -> O.Tc

E.phonon_dispersionE.electron_phononO.composite_methodO.Tc

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 1500

Non-linear; T_c sensitive to spectral function shape; inversion ill-conditioned.

Solvability C

Solver class:: EPW (Wannier-EPW interpolation); abinit + E-ph
Convergence rate q:: 2
Complexity:: principle-dependent

Specs (0)

No L2 specs registered yet for this principle.