论文标题
Eliashberg的语音介导的超导性的理论 - 当有效以及如何分解时
Eliashberg theory of phonon-mediated superconductivity -- when it is valid and how it breaks down
论文作者
论文摘要
我们根据霍尔斯坦模型最近广泛的蒙特卡罗研究，分析了2D系统中语音介导的超导性超导性的埃利亚斯贝格理论的有效性。传统观点说，只要顶点校正仍然很小，Eliashberg理论就适用。对于声子Energy $ω_0$和费米能$ e_f $的小比例，即使无量纲的电子偶联$λ$大于一个，即在强耦合方案中，这种情况也应该保持。在Migdal近似中计算的各种数量与量子蒙特卡洛计算的各种数量之间的比较证明了这种信念是错误的，并且我们从分析上确定了某些在$λ=λ_{Cr} $的“正常状态”属性发生这种崩溃的方式，其中$λ_{cr} = o（cr} = o（cr} = o（1）$。分解发生在足够高的温度下，以至于超导和电荷密度波的相关性均在任何显着的距离范围内延伸，因此它不能与不稳定性的发作相关，而不是与任何相关有序的基态相关的，而是与经典双极形成的局部物理学有关。尽管如此，我们表明，可以准确地推断出某些属性，包括$ t_c $的超导体$ t_c $和$ t_c $以下的超导差距结构，可以从$λ\leqλ_{cr} $的Eliashberg理论的强耦合限制中准确地推断出来。
We analyze the validity of Eliashberg theory of phonon-mediated superconductivity in 2D systems in light of recent extensive Monte-Carlo studies of the Holstein model. Conventional wisdom says that Eliashberg theory is applicable as long as vertex corrections remain small. For small ratio of the phonon energy $Ω_0$ and the Fermi energy $E_F$, this condition is supposed to hold even when the dimensionless electron-phonon coupling $λ$ is larger than one, i.e., in the strong coupling regime. A comparison between various quantities computed in the Migdal approximation and those computed by Quantum Monte Carlo prove that this belief is wrong, and we identify analytically some of the ways in which this breakdown occurs for various "normal state" properties at $λ= λ_{cr}$, where $λ_{cr} = O(1)$. The breakdown occurs at temperatures high enough that neither superconducting nor charge-density wave correlations extend over any significant range of distances, so it cannot be associated with the onset of an instability toward any of the relevant ordered ground-states - rather it is associated with the local physics of classical bipolaron formation. Still, we show that certain properties, including the superconducting $T_c$ and the superconducting gap structure below $T_c$, can be accurately inferred from the strong-coupling limit of Eliashberg theory at $λ\leq λ_{cr}$.
