Mott effect and screening in quantum well structures

Abstract

We consider the formation of exciton bound states between electrons and holes in a 2D layer. The medium modifications of two-particle properties are obtained from a systematic Green function approach within a cluster mean field approximation. Contributions from correlations (excitons) in the medium are given. The importance of Pauli blocking on the shift of the ionization energy of excitons in comparison to screening is shown. Effective wave equation.Electrons and holes in a two-dimensional quantum well structure interact via the Coulomb potential V eh (q) = −e 2 /(2Ω 0 r 0 q) and can form bound states, the excitons. A rigorous approach to this electron-hole-exciton system embedded into a surrounding medium in equilibrium (density n, temperature T ) can be given by the method of thermodynamic Green functions. We will follow the approach according to the monography [1], see also [2,3], where the Bethe-Salpeter equation for the propagation of a two-particle cluster was investigated. The following effective wave equation (in-medium Schrödinger equation) for the electron-hole system has been derived yielding the eigenstates Ψ αP (1, 2) and the corresponding energy eigenvalues E αP :The single-particle states are given by the quantum numbers {1} = { p 1 , σ 1 , c 1 } describing linear momentum (two dimensional), spin and species (e, h), respectively. The bound states (excitons) are characterized by the total linear momentum P and internal quantum number α. The influence of the surrounding matter on the two-particle complex is described by the plasma HamiltonianThere are two important many-particle effects. Firstly, the interaction between the free particles as well as the bound states is considered in Born approximation, taking into account the full antisymmetrization of all fermionic states, also denoted as cluster-mean field approximation (mf). Secondly, the Coulomb interaction is dynamically screened by free as well as bound states (scr) as shown in [4]. The cluster-mean field terms (the Hartree terms vanish because of charge neutrality) are given as [5]V cc (12, 1 2 )Ψ α P (12)Ψ * α P (1 2 ) g eh (E α P ), V cc (13, 1 3 )Ψ * α P (23 )Ψ α P (2 3) g cc (E α P ) ,

Dynamic Structure Factor of Dusty and Low‐Dimensional Plasmas

“…Calculations for InAs/GaInAs heterostructures [33] show a similar behaviour. Due to the smaller effective mass of the holes and electrons the excitonic window is less pronounced.…”

“…Taking first order perturbation theory, the binding energies for zero layer separation were calculated and discussed in Refs. [33,37]. The parameters for which the bound state merges into the continuum of the free particles [∆E scr 1s + ∆E Pauli 1s,P = 4R * ] are of particular interest.…”

“…The influence of the surrounding matter on the two-particle complex is described by the plasma Hamiltonian H pl eh (12, 1 2 , E αP ) as outlined in Ref. [33]. Within a clustermean field approximation, the interaction between the free particles as well as the bound states is considered.…”

“…We will follow the approach according to the monograph [29], see also [30][31][32], where the Bethe-Salpeter equation for the propagation of a two-particle cluster was investigated. The following effective wave equation (in-medium Schrödinger equation) for the electron-hole system has been derived yielding the eigenstates Ψ αP (1, 2) and the corresponding energy eigenvalues E αP [33]:…”

“…(14), for exploratory calculations of the ionization energy E ioniz αP of the exciton we performed approximations leading to [33] …”