Extra Seminar - Würzburg ToCoTronics Colloquium

The 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  ground state.  The last scenario has never been analyzed in precise quantitative terms for a generic electron density. Using variational considerations, we establish rigorous upper bounds on the coupling, at which a FL state transforms into a polaron state. We show that at small and near-maximum densities, this happens well before a dressed phonon softens.  We present analytical reasoning for this behavior based on the eikonal-type  diagrammatic treatment of the on-site Holstein model for the spin polarized case  and argue that polarons are produced by fermions with energies comparable to the bandwidth; i.e., polaron formation is outside the realm of MET.
We discuss the transformation from a Fermi liquid to a polaron state via an intermediate mixed state and  a violation of Luttinger theorem.