激子线性和非线性光学响应的规范不变性
Gauge invariance of excitonic linear and nonlinear optical response
摘要：
研究了四种不同方法计算多带半导体激子线性和非线性光学响应的等价性。这四种方法分别来自于两种测量方法，即长度测量和速度测量，以及两种计算电流密度的方法，即直接计算和通过极化密度的时间导数计算。线性和二次响应函数的所有方法，通过采用微扰密度矩阵的方法内的平均场近似。所有四种方法的等价性严格示出，当一个正确的相互作用哈密顿量采用的速度规范的方法。正确的相互作用被写为一系列包含未微扰哈密顿量和位置算符的算符，在无限库仑屏蔽和无限多能带的极限下，它等价于传统的速度规范相互作用。作为一个案例研究，该理论被应用到六方氮化硼单层膜，并在不同的方法发现的线性和非线性光学响应进行了比较。
英文摘要：
We study the equivalence of four different approaches to calculate the excitonic linear and nonlinear optical response of multiband semiconductors. These four methods derive from two choices of gauge, i.e. length and velocity gauges, and two ways of computing the current density, i.e. direct evaluation and evaluation via the time-derivative of the polarization density. The linear and quadratic response functions are obtained for all methods by employing a perturbative density matrix approach within the mean-field approximation. The equivalence of all four methods is shown rigorously, when a correct interaction Hamiltonian is employed for the velocity gauge approaches. The correct interaction is written as a series of commutators containing the unperturbed Hamiltonian and position operators, which becomes equivalent to the conventional velocity gauge interaction in the limit of infinite Coulomb screening and infinitely many bands. As a case study, the theory is applied to hexagonal boron nitride monolayers, and the linear and nonlinear optical response found in different approaches are compared.
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