Breakdown of the Migdal-Eliashberg theory and a theory of lattice-fermionic superfluidity

Article

关键词: STRONG-COUPLING LIMIT;    SUPERCONDUCTORS;    TRANSITION;    VIBRATIONS;    ELECTRONS;    MOTION;    MODEL;   

DOI  :  10.1103/PhysRevB.106.054518

来源: SCIE

【 摘 要 】

We show that the Migdal-Eliashberg theory loses validity at a finite value lambda c of the electron-phonon coupling lambda regardless of the underlying model Hamiltonian. The value of lambda c is approximately between 3.0 and 3.7. The new phase that emerges at lambda > lambda(c) 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 lambda 3.7 and the quasiparticle lifetime vanishes in the strong coupling limit. At fixed lambda > lambda(c), 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 lambda across lambda(c) 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 lambda, our theory reduces to the Migdal-Eliashberg theory, and past lambda(c), it describes the new phase and a range of other phenomena.

【 授权许可】

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