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arXiv 2301.04832cond-mat.supr-con
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超导体清洁极限下Higgs模式的光学响应:通过Eilenberger方程和Ginzburg-Landau拉格朗日量的公式化

Optical response of Higgs mode in superconductors at clean limit: formulation through Eilenberger equation and Ginzburg-Landau Lagrangian

F. Yang, M. W. Wu

AI总结:

本文通过路径积分和Keldysh形式体系下的Eilenberger方程,证明清洁极限超导体二阶光学响应中Higgs模式有限产生,澄清了Matsubara频率处理的争议。

摘要:

宏观的Ginzburg-Landau拉格朗日量和微观规范不变的动力学方程均表明,在清洁极限下超导体的二阶光学响应中存在有限的Higgs模式产生,而先前通过路径积分方法和Matsubara形式体系内的Eilenberger方程推导未能给出这种产生。导致这一争议的关键处理在于一个人为方案,即在Matsubara形式体系内处理间隙动力学时,是否将外部光学频率视为连续变量或玻色型Matsubara频率。为解决此问题,我们通过路径积分方法推导了在矢势存在下接近$T_c$时超导间隙的有效作用量,以填补超导体中Ginzburg-Landau拉格朗日量微观推导长期缺失的空白。结果表明,只有在Matsubara形式体系内将光学频率视为连续变量,才能获得基本的Ginzburg-Landau拉格朗日量,特别是,有限的Ginzburg-Landau动能项导致在清洁极限下有限的Higgs模式产生。为进一步通过独立框架消除Matsubara频率的混淆,我们应用了Keldysh形式体系内的Eilenberger方程,该体系与Matsubara空间完全无关。通过计算二阶响应中的间隙动力学,解析地证明了所涉及的光学频率是连续变量而非玻色型Matsubara频率,从而在清洁极限下产生有限的Higgs模式。

英文摘要:

Both macroscopic Ginzburg-Landau Lagrangian and microscopic gauge-invariant kinetic equation suggest a finite Higgs-mode generation in the second-order optical response of superconductors at clean limit, whereas the previous derivations through the path-integral approach and Eilenberger equation within the Matsubara formalism failed to give such generation. The crucial treatment leading to this controversy lies at an artificial scheme that whether the external optical frequency is taken as continuous variable or bosonic Matsubara frequency to handle the gap dynamics within the Matsubara formalism. To resolve this issue, we derive the effective action of the superconducting gap near $T_c$ in the presence of the vector potential through the path-integral approach, to fill the long missing blank of the microscopic derivation of the Ginzburg-Landau Lagrangian in superconductors. It is shown that only by taking optical frequency as continuous variable within the Matsubara formalism, can one achieve the fundamental Ginzburg-Landau Lagrangian, and in particular, the finite Ginzburg-Landau kinetic term leads to a finite Higgs-mode generation at clean limit. To further eliminate the confusion of the Matsubara frequency through a separate framework, we apply the Eilenberger equation within the Keldysh formalism, which is totally irrelevant to the Matsubara space. By calculating the gap dynamics in the second-order response, it is analytically proved that the involved optical frequency is a continuous variable rather than bosonic Matsubara frequency, causing a finite Higgs-mode generation at clean limit.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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