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Vertex corrections for impurity scattering at a ferromagnetic quantum critical point

机译：在铁磁量子临界点进行杂质散射的顶点校正

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摘要

We study the renormalization of a nonmagnetic impurity's scattering potential due to the presence of a massless collective spin mode at a ferromagnetic quantum critical point. To this end, we compute the lowest-order vertex corrections in two- and three-dimensional systems for arbitrary scattering angle and frequency of the scattered fermions, as well as band curvature. We show that only for backward scattering in D=2 does the lowest-order vertex correction diverge logarithmically in the zero-frequency limit. In all other cases, the vertex corrections approach a finite (albeit possibly large) value for ω→0. We demonstrate that vertex corrections are strongly suppressed with increasing curvature of the fermionic bands. Moreover, we show how the frequency dependence of vertex corrections varies with the scattering angle. We also discuss the form of higher order ladder vertex corrections and show that they can be classified according to the zero-frequency limit of the lowest-order vertex correction. Finally, we suggest that the combined frequency and angular dependence of vertex corrections might be experimentally observable via a combination of frequency dependent and local measurements, such as scanning tunneling spectroscopy on ordered impurity structures, or measurements of the frequency-dependent optical conductivity.
机译：我们研究了由于在铁磁量子临界点处存在无质量集体自旋模态而导致的非磁性杂质散射势的重新归一化。为此，我们在二维和三维系统中针对散射费米子的任意散射角和频率以及能带曲率计算了最低阶的顶点校正。我们表明，仅对于D = 2中的向后散射，最低阶顶点校正才会在零频率范围内以对数形式发散。在所有其他情况下，对于ω→0，顶点校正都接近有限值（尽管可能很大）。我们证明，随着费米离子带的曲率的增加，顶点校正被强烈抑制。此外，我们显示了顶点校正的频率依赖性如何随散射角变化。我们还讨论了高阶阶梯顶点校正的形式，并表明它们可以根据最低阶顶点校正的零频率极限进行分类。最后，我们建议可以通过结合频率相关和局部测量（例如对有序杂质结构进行扫描隧道光谱法或对频率相关的光导率进行测量）来通过实验观察到顶点校正的组合频率和角度相关性。

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