Speaker
Description
Migdal-Eliashberg theory (MET) describes electrons interacting with phonons in the adiabatic limit when the phonon Debye frequency is much smaller than the Fermi energy. A conventional belief is that MET holds even at strong coupling, when electron self-energy is large, and breaks down only near the point where the dressed phonon spectrum softens to near zero. We analyze numerically and analytically a different option---collapse to a polaronic/bipolaronic ground state. The last scenario has never been analyzed in precise quantitative terms for a generic electron density. We establish rigorous upper bounds on the coupling, at which the Fermi liquid state transforms into the bipolaron (polaron) state, and show that at small and near-maximum densities, this happens well before a dressed phonon softens. This is true both in 2D and 3D systems; in the latter the upper bound on coupling tends to zero (!) in the limit of small or near-full density, indicating that polaron formation cannot be captured by MET and textbook treatment of e-ph problem in continuum is ill-defined. Close to half-filling, the leading instability upon increasing coupling is towards a charge-density-wave.