半导体空穴液体的介电函数：全频率和波矢依赖性
Dielectric function of the semiconductor hole liquid: Full frequency and wave vector dependence
摘要：
本文在无规相位近似下研究了p掺杂Ⅲ-Ⅴ族锌半导体的均匀半导体空穴液体的介电函数。空穴系统的单粒子物理模型采用Luttinger的四带哈密顿量球近似。对于库仑相互作用的空穴液体，零温介电函数的波矢和频率的完全依赖性进行了探索。介电函数的虚部解析地获得在复杂的，但完全基本的表达式，而在实部的非基本的一维积分的结果仍然有待执行。这两个独立的计算的正确性检查通过Kramers-Kronig关系。重空穴和轻空穴之间的质量差，以及背景介电常数的变化，导致等离子体激元激发模式的剧烈变化，一般来说，可以识别出两个等离子体激元分支。这些发现是全介电功能评估的结果，无法通过高频扩展获得。在静态极限下，重、轻空穴的费米波数之间存在弗里德尔振荡的拍频。
英文摘要：
We study the dielectric function of the homogeneous semiconductor hole liquid of p-doped bulk III-V zinc-blende semiconductors within random phase approximation. The single-particle physics of the hole system is modeled by Luttinger's four-band Hamiltonian in its spherical approximation. Regarding the Coulomb-interacting hole liquid, the full dependence of the zero-temperature dielectric function on wave vector and frequency is explored. The imaginary part of the dielectric function is analytically obtained in terms of complicated but fully elementary expressions, while in the result for the real part nonelementary one-dimensional integrations remain to be performed. The correctness of these two independent calculations is checked via Kramers-Kronig relations. The mass difference between heavy and light holes, along with variations in the background dielectric constant, leads to dramatic alternations in the plasmon excitation pattern, and generically, two plasmon branches can be identified. These findings are the result of the evaluation of the full dielectric function and are not accessible via a high-frequency expansion. In the static limit a beating of Friedel oscillations between the Fermi wave numbers of heavy and light holes occurs.
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