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arXiv 1609.07285cond-mat.supr-con
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涡旋玻璃中的涡旋光谱学:实空间数值方法

Vortex spectroscopy in the vortex glass: A real-space numerical approach

C. Berthod

摘要:

本文提出了一种求解具有任意分布涡系的Bogoliubov-de Gennes方程的方法。基于切比雪夫多项式的实空间格林函数方法是补充规范变换,它允许一个治疗有限以及无限,有序以及无序的涡旋配置。该工具在非常低的磁场和玻璃相下提供了前所未有的涡旋晶格。在详细描述了该方法及其实现之后,我们用它解决了一系列与正方晶格上的$d$波超导性有关的问题。我们首先研究了涡旋核能谱的连续性及其从量子态到半经典极限的演化,然后通过Lifshitz跃迁研究了能带结构对涡旋的影响,接着研究了涡旋晶格随场的减小而向孤立涡旋极限的演化,并指出一个新的长度尺度控制着这种跃迁。最后,我们对涡旋晶格中存在位置无序时的涡旋核局域态密度进行了统计研究。计算揭示了一些性质的差异,在量子和半经典制度的涡旋。

英文摘要:

A method is presented to solve the Bogoliubov-de Gennes equations with arbitrary distributions of vortices. The real-space Green's function approach based on Chebyshev polynomials is complemented by a gauge transformation which allows one to treat finite as well as infinite, ordered as well as disordered vortex configurations. This tool gives unprecedented access to vortex lattices at very low magnetic fields and glassy phases. After describing in detail the method and its implementation, we use it to address a series of problems related to $d$-wave superconductivity on the square lattice. We first study the continuity of the vortex-core energy spectrum and its evolution from the quantum regime to the semiclassical limit; we investigate the effect of the band structure on the vortex by following the self-consistent solution through a Lifshitz transition; we then study the evolution from the vortex lattice to the isolated-vortex limit with decreasing field and show that a new emerging length scale controls this transition; finally, we perform a statistical study of the vortex-core local density of states in the presence of positional disorder in the vortex lattice. The calculations reveal a number of qualitative differences between the properties of vortices in the quantum and semiclassical regimes.

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