Migdal approximation

E59621

approximation in electron-phonon theory approximation in many-body physics theoretical approximation

The Migdal approximation is a theoretical simplification in many-body physics that neglects vertex corrections in electron-phonon interactions, justified when phonon energies are much smaller than electronic energies.

Aliases (1)

Migdal theorem ×1

Statements (44)

Predicate	Object
instanceOf	approximation in electron-phonon theory → approximation in many-body physics → theoretical approximation →
appliesTo	electron-phonon interactions →
assumes	electrons respond much faster than lattice vibrations → phonon energies are much smaller than electronic energies → small ratio of phonon frequency to Fermi energy →
basedOn	separation of energy scales between electrons and phonons →
contrastsWith	approaches including full vertex corrections →
field	condensed matter physics → many-body physics →
formalism	Feynman diagram expansion → many-body Green's function theory →
goal	make electron-phonon problems analytically and numerically tractable →
historicallyAttributedTo	Arkady Migdal →
implies	electron-phonon coupling can be treated perturbatively → vertex corrections are of higher order in small mass ratio →
justifiedWhen	Migdal parameter is small → ion mass is much larger than electron mass →
mayBreakDownWhen	electron-phonon coupling is very strong → phonon energies become comparable to electronic energies → systems are non-adiabatic →
neglects	higher-order electron-phonon scattering processes involving vertex corrections → vertex corrections in electron-phonon interaction diagrams →
relatedConcept	Migdal-Eliashberg theory → adiabatic limit → electron-phonon self-energy → mass renormalization parameter lambda →
relatedTo	Migdal theorem →
simplifies	diagrammatic treatment of electron-phonon interactions → self-consistent calculations in Eliashberg theory →
timePeriod	mid-20th century →
usedFor	computing superconducting transition temperatures in conventional superconductors → describing electron lifetime due to electron-phonon scattering → describing quasiparticle mass renormalization by phonons →
usedIn	Eliashberg theory → calculations of electron self-energy due to phonons → calculations of phonon-induced renormalization of electronic bands → first-principles calculations of electron-phonon coupling in metals → theory of conventional superconductivity → theory of phonon-mediated pairing in superconductors →
uses	lowest-order electron-phonon self-energy diagrams →
validityDependsOn	adiabatic approximation → smallness of characteristic phonon frequency compared to Fermi energy →

Referenced by (2)

Subject (surface form when different)	Predicate
Eliashberg theory →	assumes
Migdal approximation ("Migdal theorem") →	relatedTo