狄拉克超导体中的规范不变性、集体模式与正常态减法的合理性

中文摘要 AI 辅助

在狄拉克超导体中，低能狄拉克模型的无界谱会导致深层态对电磁响应产生非物理的带间贡献。为消除这些贡献，正常态减法（NSS）被广泛采用，该方法将超导态响应减去正常态响应。然而，NSS与规范不变电磁响应的关系，尤其是沃德恒等式要求的顶点修正的作用，仍不清楚。本研究考虑具有s波配对的质量狄拉克模型，通过求解Bethe–Salpeter方程并将集体模式贡献纳入电磁顶点，解析研究零温下的电磁响应。结果表明，在静态长波极限下，顶点修正与NSS的裸纵向响应精确抵消，得到规范不变性要求的消失的纵向响应；而顶点修正的横向分量在长波极限下消失，因此规范不变的迈斯纳权重与NSS的裸横向响应结果一致。此外，在各向同性且解析的紫外正则化项类别中，静态长波极限下的正则化项被规范不变性唯一确定为NSS规定的值。本研究为NSS提供了微观层面的合理性依据。

英文摘要

In Dirac superconductors, the unbounded spectrum of low-energy Dirac models is known to give rise to unphysical interband contributions from deep-lying states to the electromagnetic response. To eliminate these contributions, normal-state subtraction (NSS), in which the normal-state response is subtracted from the superconducting-state response, has been widely employed. However, the relation between NSS and a gauge-invariant electromagnetic response, particularly the role of the vertex correction required by the Ward identity, has remained unclear. In this work, we consider a massive-Dirac model with $s$-wave pairing and analytically investigate the electromagnetic response at zero temperature by solving the Bethe--Salpeter equation and incorporating the collective-mode contribution to the electromagnetic vertex. We show that, in the static long-wavelength limit, the vertex correction exactly cancels the bare longitudinal response with NSS, yielding the vanishing longitudinal response required by gauge invariance. In contrast, the transverse component of the vertex correction vanishes in the long-wavelength limit, so that the gauge-invariant Meissner weight coincides with that obtained from the bare transverse response with NSS. Moreover, within the class of isotropic and analytic UV regularization terms, we show that gauge invariance uniquely fixes the regularization term in the static long-wavelength limit to the value prescribed by NSS. Our results thus provide a microscopic justification for NSS.

补充信息

备注

14 pages, no figures