Migdal-Eliashberg theory breaks down to polaron/bipolaron states before phonon softening at extreme densities, with variational upper bounds on coupling λ showing this occurs well before softening in 2D/3D systems.
Both containλ 2 0 in the prefactors, and in the calculations to this order, the renormalization ofµ 0 into µcan be neglected
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Breakdown of the Migdal-Eliashberg theory for electron-phonon systems. Role of polarons/bi-polarons
Migdal-Eliashberg theory breaks down to polaron/bipolaron states before phonon softening at extreme densities, with variational upper bounds on coupling λ showing this occurs well before softening in 2D/3D systems.