We show that the Migdal-Eliashberg theory loses validity at a finite value λc of the electron-phonon coupling λ regardless of the underlying model Hamiltonian. The value of λc is approximately between 3.0 and 3.7. The new phase that emerges at λ>λc breaks the lattice translational symmetry. Depending on the filling fraction and crystal symmetry, it is an insulator or a Fermi liquid. Its characteristic feature is a gap or a pronounced depression of the fermionic density of states near the Fermi level. We establish the breakdown from within the Migdal-Eliashberg theory by demonstrating that the normal state specific heat is negative for λ≥3.7 and the quasiparticle lifetime vanishes in the strong coupling limit. At fixed λ>λc, the transition to the new phase occurs at a critical temperature higher than the superconducting transition temperature. In addition, there is a first-order phase transition between the new phase and the superconducting state as we vary λ across λc at fixed temperature. We put forward a new theory - lattice-fermionic theory of superfluidity - that bridges the gap between the Migdal-Eliashberg approach and the physics at stronger coupling. At small λ, our theory reduces to the Migdal-Eliashberg theory, and past λc, it describes the new phase and a range of other phenomena.
All Science Journal Classification (ASJC) codes
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics