发表机构
Kent State University; Rutgers University（肯特州立大学; 罗格斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究揭示Eliashberg超导体中，声子推迟效应解除了BCS理论中希格斯模式与对破缺阈值的简并，使其成为持续振荡的亚能隙激发，而非衰减的边缘奇点。
AI 中文摘要
在超导BCS理论中，振幅（希格斯）模式与对破缺阈值简并，其频率与2Δ重合，因此属于边缘奇点而非真正的集体模式，这就是为何在t=0时刻施加微弱突扰后，其振荡会以1/√t的形式代数衰减。我们证明，强耦合理论中声子动力学导致的推迟效应会解除这种简并：希格斯模式从由能隙Δ_g决定的对破缺边缘2Δ_g脱离，成为尖锐的亚能隙激发。我们利用具有爱因斯坦声子谱的Migdal-Eliashberg理论的Eilenberger方程，直接在实频率轴上计算纵向对 susceptibility以确定其频率。质量重整化的响应提供了至少五分之二的位移，甚至可能提供全部位移：若关闭该响应，结合能会低于计算的分辨率。然而其影响显著：百分级的位移会将振幅通道约四分之一的谱重从两准粒子连续区转移到离散能级，因此实验观测到的并非位移本身，而是其后果：持续而非以1/√t衰减的振幅振荡。
英文摘要
In the BCS theory of superconductivity the amplitude (Higgs) mode is degenerate with the pair-breaking threshold: its frequency coincides with $2Δ$, so it is an edge singularity rather than a true collective mode. This is why after a sudden weak perturbation at $t=0$ its oscillations decay algebraically as $1/\sqrt{t}$. We show that the retardation effects due to the phonon dynamics in the strong-coupling theory lift this degeneracy. The Higgs mode detaches from the pair-breaking edge $2Δ_g$, set by the spectral gap, and becomes a sharp subgap excitation. We determine its frequency from the longitudinal pair susceptibility evaluated directly on the real frequency axis, using the Eilenberger equations for Migdal--Eliashberg theory with the Einstein phonon spectrum. The response of the mass renormalization supplies at least two fifths of the displacement, and possibly all of it: with it switched off, the binding falls below the resolution of the calculation. Its consequences, however, are significant because a percent-level shift transfers about a quarter of the spectral weight of the amplitude channel out of the two-quasiparticle continuum into a discrete energy level. What experiment sees is therefore not the displacement itself but its consequence: amplitude oscillations that persist instead of decaying as $1/\sqrt{t}$.
Comments39 pages, 8 figures
