论文标题
Migdal-Eliashberg理论的崩溃和晶格 - 弗洛米奇超流体的理论
Breakdown of the Migdal-Eliashberg theory and a theory of lattice-fermionic superfluidity
论文作者
论文摘要
我们表明，Migdal-Eliashberg理论在有限的值$λ_c$的电子耦合$λ$的情况下失去了有效性，而不论基础模型hamiltonian。 $λ_C$的值大约在3.0到3.7之间。以$λ>λ_c$出现的新阶段打破了晶格翻译对称性。根据填充部分和晶体对称性，它是绝缘子或费米液体。它的特征是在费米水平附近状态的费米密度的缝隙或明显的凹陷。我们通过证明$λ\ ge 3.7 $的正常状态特异性热量为负面，而准粒子寿命在强耦合极限中消失，我们从Migdal-Eliashberg理论中建立了分解。在固定的$λ>λ_c$时，向新相的过渡发生在高于超导过渡温度的临界温度下。此外，由于我们在固定温度下在$λ_c$上改变了$λ$，因此新阶段和超导状态之间存在一阶相变。我们提出了一种新的理论 - 晶格 - 弗拉米斯的超流体理论 - 弥合了Migdal -Eliashberg方法与物理学之间的差距。在小$λ$的情况下，我们的理论减少了Migdal-Eliashberg理论，并且过去$λ_C$，它描述了新阶段和一系列其他现象。
We show that the Migdal-Eliashberg theory loses validity at a finite value $λ_c$ of the electron-phonon coupling $λ$ regardless of the underlying model Hamiltonian. The value of $λ_c$ is approximately between 3.0 and 3.7. The new phase that emerges at $λ>λ_c$ 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 $λ\ge 3.7$ and the quasiparticle lifetime vanishes in the strong coupling limit. At fixed $λ>λ_c$, 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 $λ$ across $λ_c$ 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 $λ$, our theory reduces to the Migdal-Eliashberg theory and, past $λ_c$, it describes the new phase and a range of other phenomena.
