A solvable model for excitonic complexes in one dimension
A solvable model for excitonic complexes in one dimension
复制标题
一维激子配合物的可解模型
DOI：
10.1063/1.532082
复制
发表时间：
1997
期刊：
影响因子：
--
通讯作者：
N. Johnson
中科院分区：
文献类型：
--
作者：
A. Markvardsen;N. Johnson
实验表明，低维半导体纳米结构中可以存在包含带负电的电子（e）和带正电的空穴（h）的稳定的少体团簇。除了熟悉的激子（e+h）之外，还观察到了三体“带电激子”（2e+h 和 2h+e）。人们对这种带电激子的性质知之甚少，因为三体问题通常很难解决，即使是在数值上也是如此。在这里，我们引入一个简单的模型，可以被视为扩展的Calogero模型，用于分析计算一维纳米结构（例如有限长度量子线）中带电激子和中性激子的能谱。除了其物理动机之外，该模型还具有数学意义，因为它可以与 Heun（或 Heine）方程相关，并且如明确所示，可以获得高度准确的封闭形式解。
It is known experimentally that stable few-body clusters containing negatively-charged electrons (e) and positively-charged holes (h) can exist in low-dimensional semiconductor nanostructures. In addition to the familiar exciton (e+h), three-body “charged excitons” (2e+h and 2h+e) have also been observed. Much less is known about the properties of such charged excitons since three-body problems are generally very difficult to solve, even numerically. Here we introduce a simple model, which can be considered as an extended Calogero model, to calculate analytically the energy spectra for both a charged exciton and a neutral exciton in a one-dimensional nanostructure, such as a finite-length quantum wire. Apart from its physical motivation, the model is of mathematical interest in that it can be related to the Heun (or Heine) equation and, as shown explicitly, highly accurate, closed form solutions can be obtained.