超越共振原理的II型泵浦：从能量规则到几何规则
Type-II pumping beyond resonance principle: From energetic to geometric rules
AI总结：
本文提出几何泵浦（GP）作为超越能量共振的II型泵浦机制，阐明其分数性、不可逆性及对拓扑相变的依赖，并通过ZrTe₅相干声子驱动的超快光谱实验验证其可检测特征。
摘要：
传统上，泵浦依赖于能量共振：能量量子 ${\hbar}ω$ 与能隙 $Δ$ 相匹配。在线性近似下，这被称为费米黄金规则（FGR）。然而，这一原理在“0/0”极限下变得难以应用，即 $ω,Δ{\rightarrow}0$ 同时趋于零。在“0/0”情形中，例如拓扑相变（TPT），一种II型泵浦——几何泵浦（GP）——被确认遵循几何规则，区别于由FGR支配的I型泵浦。I型具有“能量箭头”特征，将粒子推向更高能量，这反映在FGR对费米分布 $f_v-f_c$（价带和导带的占据概率）的依赖上。而GP是非定向的，其概率依赖于 $f_v+f_c-2f_v f_c$，这是检测的关键特征。在本工作中，我们讨论：（1）GP的概念；（2）其分数性、不可逆性以及对TPT依赖性的特征；（3）在ZrTe$_5$相干声子驱动下利用超快光谱进行实验检测。
英文摘要：
Conventionally, pumping relies on energetic resonance: energy quanta ${\hbar}ω$ matches the gap $Δ$. Under linear approximation, this is known as the Fermi golden rule (FGR). However, this principle becomes challenging to apply in the "0/0" limit, where $ω,Δ{\rightarrow}0$ simultaneously. In "0/0" scenarios, such as topological phase transition (TPT), a type-II pumping, geometric pumping (GP), is recognized subject to geometric rules, distinguished from type-I dictated by FGR. Type-I features an "arrow of energy", sending particles higher in energy, reflected by FGR's dependence on Fermi distribution $f_v-f_c$ (probabilities of valence and conduction bands). While GP is non-directional, its probability relies on $f_v+f_c-2f_v f_c$ instead, a key signature for detection. In this work, we address: (1) the concept of GP; (2) its features of fractionality, irreversibility, and dependence on TPT; (3) experimental detection with ultra-fast spectrum in coherent phonon driving of ZrTe$_5$.
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