中心对称电子系统中的非线性太赫兹电光响应
Nonlinear terahertz electro-optical responses in centrosymmetric electronic systems
AI总结：
本文回顾并扩展了计算中心对称系统有限频率非线性电光响应的场论形式体系，通过因果响应函数与虚时序电流关联函数的精确映射，证明了非线性电导率的广义$f$-求和规则，并成功应用于计算弱无序非相互作用电子系统的规范不变非线性电导率及太赫兹Kerr信号。
摘要：
受近期使用泵浦-探测装置研究关联电子材料的太赫兹光谱学发展的启发，我们回顾了场论形式体系，从基本的时间依赖微扰理论出发，计算中心对称系统中的有限频率非线性电光响应。我们将非线性电流核表示为若干因果响应函数之和。这些因果函数无法使用微扰场论方法来计算，因为它们不是回路序的。因此，我们将每个响应函数与相应的虚时序电流关联函数联系起来，因为后者可以使用 Wick 定理进行因子分解。响应函数与关联函数之间的映射（适当地解析延拓到实频率）被精确证明。我们推导了非线性电流核满足的约束条件，并证明了非线性电导率的广义 $f$-求和规则，所有这些都是粒子数守恒的结果。这些约束保证了非线性静态响应免受虚假发散的影响。我们应用该理论计算了在弱无序存在下非相互作用电子系统的规范不变非线性电导率。作为这种广义非线性响应的特例，我们讨论了其三次谐波和瞬时太赫兹 Kerr 信号。该形式体系可用于计算电子系统对称性破缺相（如超导体、密度波和向列态）中的非线性电导率。
英文摘要：
Motivated by the recent developments in terahertz spectroscopy using pump-probe setups to study correlated electronic materials, we review the field theoretical formalism to compute finite frequency nonlinear electro-optical responses in centrosymmetric systems starting from basic time dependent perturbation theory. We express the nonlinear current kernel as a sum of several causal response functions. These causal functions cannot be evaluated using perturbative field theory methods, since they are not contour ordered. Consequently, we associate each response function with a corresponding imaginary time ordered current correlation function, since the latter can be factorized using Wick's theorem. The mapping between the response functions and the correlation functions, suitably analytically continued to real frequencies, is proven exactly. We derive constraints satisfied by the nonlinear current kernel and we prove a generalized $f$-sum rule for the nonlinear conductivity, all of which are consequences of particle number conservation. The constraints guarantee that the nonlinear static responses are free from spurious divergences. We apply the theory to compute the gauge invariant nonlinear conductivity of a system of noninteracting electrons in the presence of weak disorder. As special cases of this generalized nonlinear response, we discuss its third harmonic and its instantaneous terahertz Kerr signals. The formalism can be used to compute the nonlinear conductivity in symmetry broken phases of electronic systems such as superconductors, density waves and nematic states.
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