论文标题
以非线性顺序统一半典型和量子扰动理论
Unifying semiclassics and quantum perturbation theory at nonlinear order
论文作者
论文摘要
非线性电响应允许独特的窗口进入带结构几何形状的影响。可以从小频率的玻尔兹曼方法开始，或者使用久保的公式以有限的频率进行共振。但是，尚未建立两种方法之间的确切联系。为了关注二阶非线性响应，我们在这里展示了如何从速度仪表仪中的扰动理论中恢复半经典限制，只要考虑到有限的准粒子寿命。我们发现与带状几何相关的矩阵元素在此极限中结合在一起，以产生半经典的非线性电导率。我们通过在放松时间$τ$中对非线性电导率的量子贡献$τ^{ - 1} $来证明新形式主义的力量，这在Boltzmann方法中主要是无法访问的。我们概述了哪些步骤可以推广到应用扰动中的更高订单，并评论我们结果的潜在实验签名。
Nonlinear electrical response permits a unique window into effects of band structure geometry. It can be calculated either starting from a Boltzmann approach for small frequencies, or using Kubo's formula for resonances at finite frequency. However, a precise connection between both approaches has not been established. Focusing on the second order nonlinear response, here we show how the semiclassical limit can be recovered from perturbation theory in the velocity gauge, provided that finite quasiparticle lifetimes are taken into account. We find that matrix elements related to the band geometry combine in this limit to produce the semiclassical nonlinear conductivity. We demonstrate the power of the new formalism by deriving a quantum contribution to the nonlinear conductivity which is of order $τ^{-1}$ in the relaxation time $τ$, which is principally inaccessible within the Boltzmann approach. We outline which steps can be generalized to higher orders in the applied perturbation, and comment about potential experimental signatures of our results.
