标题： 非线性电磁响应的量子理论 显示英文标题

标题： Quantum theory of nonlinear electromagnetic response

摘要： 近年来，由于其在阐明物质量子特性方面的潜力，非线性电磁响应的研究受到了广泛关注。 尽管在发展电场非线性响应的量子理论方面取得了显著进展，但尚未有全面的量子理论框架系统地讨论电场和磁场的非线性响应。 在此，我们使用Matsubara格林函数方法，提出了一种系统的非线性电磁响应量子理论，该理论明确包含了外部电磁场的波矢依赖性。 我们提供了图示表示，并揭示了输运系数的一般性质。 我们将该理论应用于二阶响应，推导出了时间反演对称和破坏系统中的非线性霍尔效应和磁非线性霍尔效应。 这些效应来源于多种量子几何来源。 此外，我们分析了来自Zeeman相互作用的贡献。 我们的工作提出了一个统一的非线性电磁响应量子理论，为该领域进一步探索新现象铺平了道路。 显示英文摘要

摘要： In recent years, the investigation of nonlinear electromagnetic responses has received significant attention due to its potential for elucidating the quantum properties of matter. Although remarkable progress has been achieved in developing quantum theories of nonlinear responses to electric field, a comprehensive quantum theory framework that systematically addresses nonlinear responses to both electric and magnetic fields has yet to be thoroughly discussed. Here, we present a systematic quantum theory of nonlinear electromagnetic response using the Matsubara Green's function approach, which explicitly incorporates the wave vector dependence of external electromagnetic fields. We provide diagrammatic representation and reveal the general properties of transport coefficients. We apply our theory to second-order responses, deriving the nonlinear Hall effects and magneto-nonlinear Hall effects in both time-reversal symmetric and time-reversal breaking systems. These effects stem from diverse quantum geometric sources. Additionally, we analyze the contributions arising from the Zeeman interaction. Our work presents a unified quantum theory of nonlinear electromagnetic response, paving the way for further exploration of novel phenomena in this field.