Excitonic Eigenstates of Disordered Semiconductor Quantum Wires:Adaptive Wavelet Computation of Eigenvalues for the Electron-Hole Schrodinger Equation  

作　　者：Christian Mollet Angela Kunoth Torsten Meier 

机构地区：[1]Institut fur Mathematik,Universitat Paderborn,Warburger Str.100,D-33098 Paderborn,Germany [2]Department Physik,Universitat Paderborn,Warburger Str.100,D-33098 Paderborn,Germany

出　　处：《Communications in Computational Physics》2013年第6期21-47,共27页计算物理通讯（英文）

基　　金：supported in part by the Institute for Mathematics and its Applications(IMA)at the University of Minnesota with funds provided by the National Science Foundation(NSF);supported by the Deutsche Forschungsgemeinschaft(DFG).

摘　　要：A novel adaptive approach to compute the eigenenergies and eigenfunctions of the two-particle(electron-hole)Schrodinger equation including Coulomb attraction is presented.As an example,we analyze the energetically lowest exciton state of a thin one-dimensional semiconductor quantum wire in the presence of disorder which arises from the non-smooth interface between the wire and surrounding material.The eigenvalues of the corresponding Schrodinger equation,i.e.,the onedimensional exciton Wannier equation with disorder,correspond to the energies of excitons in the quantum wire.The wavefunctions,in turn,provide information on the optical properties of the wire.We reformulate the problem of two interacting particles that both can move in one dimension as a stationary eigenvalue problem with two spacial dimensions in an appropriate weak form whose bilinear form is arranged to be symmetric,continuous,and coercive.The disorder of the wire is modelled by adding a potential in the Hamiltonian which is generated by normally distributed random numbers.The numerical solution of this problem is based on adaptive wavelets.Our scheme allows for a convergence proof of the resulting scheme together with complexity estimates.Numerical examples demonstrate the behavior of the smallest eigenvalue,the ground state energies of the exciton,together with the eigenstates depending on the strength and spatial correlation of disorder.

关 键 词：Semiconductor quantum wire disorder Schrodinger equation eigenvalue problem weak formulation bounded and coercive bilinear form adaptive wavelet method convergence complexity ground state energies EXCITON 

分 类 号：O17[理学—数学]