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arXiv 0904.0252cond-mat.str-elcond-mat.mes-hall
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铁磁量子临界点杂质散射的顶点修正

Vertex corrections of impurity scattering at a ferromagnetic quantum critical point

Enrico Rossi, Dirk K. Morr

摘要:

研究了在铁磁量子临界点处由于无质量集体自旋模的存在而引起的非磁性杂质散射势的重整化。为此,我们计算在二维和三维系统的最低阶顶点校正,任意散射角和频率的散射费米子,以及带曲率。我们表明,只有在D=2的后向散射的最低阶顶点校正发散几何在零频率的限制。在所有其他情况下,顶点校正接近零频率极限中的有限(尽管可能很大)值。我们表明,顶点修正强烈抑制与费米带的曲率增加。此外,我们还展示了顶点修正的频率依赖性如何随散射角的变化而变化。我们还讨论了高阶梯形顶点修正的形式,并表明它们可以根据最低阶顶点修正的零频率极限进行分类。我们表明,即使在这些情况下,后者是有限的,总结了一个无限系列的梯形顶点图可以导致一个强大的增强(或发散)的杂质的散射潜力。最后,我们建议,组合的频率和角度依赖的顶点校正可能是实验观察到的频率相关的和本地的测量,如扫描隧道光谱有序杂质结构,或测量的频率相关的光学电导率的组合。

英文摘要:

We study the renormalization of a non-magnetic 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 in the zero frequency limit. 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. We show that even in those cases where the latter is finite, summing up an infinite series of ladder vertex diagrams can lead to a strong enhancement (or divergence) of the impurity's scattering potential. 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.

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