无序超导体中振幅施密德-希格斯模式的空间分辨动力学

P. A. Nosov, E. S. Andriyakhina, I. S. Burmistrov
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摘要

我们研究了无序巴丁-库珀-施里弗(BCS)超导体和费米子超流体中集体振幅施密德-希格斯(SH)模式的空间分辨动力学。我们确定了一些情况,在这些情况中,长时SH响应是由平均SH感度中的一个极点决定的,该极点位于其黎曼面的非物理片上。通过对双粒子分支切割的分析延续,我们得到了与该极点相关的 SH 模式的零温色散关系和阻尼率。当相干长度明显超过平均自由路径时,极点 "隐藏 "在2\Delta$处的双粒子连续边之后,导致晚期的SH振荡以1/t^2$的频率2\Delta$衰减。尽管如此,极点会在高于 2\Delta$ 的频率上诱发迟滞的 SHs 感性峰值,并在晚期和长距离上引起动态指数为 $z=4$ 的亚扩散振荡。相反,固定频率为$\omega$的长距离振荡只有在$\omega$超过2\Delta$时才会发生,其空间周期在阈值处发散为1/(\omega - 2\Delta)^{1/4}$,最高可达对数因子。当相干长度与平均自由路径相当时,极点会重新出现在连续体中,从而在频率高于 2 (Δ$)的固定波矢量上产生额外的晚期振荡。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Spatially-resolved dynamics of the amplitude Schmid-Higgs mode in disordered superconductors
We investigate the spatially-resolved dynamics of the collective amplitude Schmid-Higgs (SH) mode in disordered Bardeen-Cooper-Schrieffer (BCS) superconductors and fermionic superfluids. We identify cases where the long-time SH response is determined by a pole in the averaged SH susceptibility, located on the unphysical sheet of its Riemann surface. Using analytic continuation across the two-particle branch cut, we obtain the zero-temperature dispersion relation and damping rate of the SH mode linked to this pole. When the coherence length significantly exceeds the mean free path, the pole is ``hidden'' behind the two-particle continuum edge at $2\Delta$, leading to SH oscillations at late times decaying as $1/t^2$ with frequency $2\Delta$. Nevertheless, the pole induces a peak in the retarded SH susceptibility at a frequency above $2\Delta$ and causes sub-diffusive oscillations with a dynamical exponent $z=4$ at both late times and long distances. Conversely, long-distance oscillations at a fixed frequency $\omega$ occur only for $\omega$ exceeding $2\Delta$, with a spatial period diverging at the threshold as $1/(\omega - 2\Delta)^{1/4}$, up to logarithmic factors. When the coherence length is comparable to the mean free path, the pole can reemerge into the continuum, resulting in additional late-time oscillations at fixed wave vectors with frequencies above $2\Delta$.
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