标题： 关于量子度量诱导的非线性输运的澄清 显示英文标题

标题： A Clarification on Quantum-Metric-Induced Nonlinear Transport

摘要： 多年来，与量子几何张量的虚部相关的贝里曲率对物理学的许多分支产生了深远的影响。 最近，作为量子几何张量实部的量子度规已被认为在全面表征凝聚态系统固有性质中是不可或缺的。 由量子度规引起的固有二阶非线性电导率最近引起了广泛关注。 然而，其表达式在文献中有所不同。 在此，我们通过系统地使用标准微扰理论、波包动力学和Luttinger-Kohn方法来解决这一差异。 此外，受狄拉克模型的启发，我们提出一个玩具模型，该模型抑制由贝里曲率引起的非线性输运，使其适用于研究由量子度规引起的非线性电导率。 我们的理论可以进一步扩展以包括无序效应和高阶量子几何贡献，为更全面和系统的理解非线性输运铺平道路。 显示英文摘要

摘要： Over the years, Berry curvature, which is associated with the imaginary part of the quantum geometric tensor, has profoundly impacted many branches of physics. Recently, quantum metric, the real part of the quantum geometric tensor, has been recognized as indispensable in comprehensively characterizing the intrinsic properties of condensed matter systems. The intrinsic second-order nonlinear conductivity induced by the quantum metric has attracted significant recent interest. However, its expression varies across the literature. Here, we reconcile this discrepancy by systematically examining the nonlinear conductivity using the standard perturbation theory, the wave packet dynamics, and the Luttinger-Kohn approach. Moreover, inspired by the Dirac model, we propose a toy model that suppresses the Berry-curvature-induced nonlinear transport, making it suitable for studying the quantum-metric-induced nonlinear conductivity. Our theory can be further extended to include disorder effects and higher-order quantum geometric contributions, paving the way for a more comprehensive and systematic understanding of nonlinear transport.