Trions in Coupled Quantum Wells and Wigner Crystallization

Abstract

We consider a restricted three body problem, where two interacted particles are located in two dimensional (2D) plane and interact with the third one located in the parallel spatially separated plane. The system of such type can be formed in the semiconductor coupled quantum wells, where the electrons (or holes) and direct excitons spatially separated in different parallel neighboring quantum wells that are sufficiently close to interact and form negative X − or positive X + indirect trions. It is shown that at large interwell separations, when the interwell separation much greater than the exciton Bohr radius, this problem can be solved analytically using the cluster approach. Analytical results for the energy spectrum and the wave functions of the spatially indirect trion are obtained, their dependence on the interwell separations is analyzed and a conditional probability distribution is calculated. The formation of 2D Wigner crystal of trions at the low densities is predicted. It is shown that the critical density of the formation of the trion Wigner crystal is sufficiently greater than the critical density of the electron Wigner crystal. PACS numbers: 71.35.Pq, 71.35.-y, 73.21.Fg I. INTRODUCTIONThe linear and nonlinear properties of semiconductor heterostructures are often governed by excitons that are defined as the bounded state of the electron-hole pair. This is especially important for semiconductors with widebandgap, where the excitonic binding energy is comparable to room temperature. Positively (X + ) and negatively (X − ) charged excitons, called trions in semiconductor structures, have been the subject of many experimental and theoretical studies in the last years. Positively charges excitons are formed by one electron and two holes, and negatively charged excitons are formed by two electrons and one hole. The theoretical proof of the stability of trions in bulk semiconductors was presented by Lampert [1]. The experimental observation of trions in semiconductor quantum wells (QWs) was achieved in CdTe/CdZnTe [2] and in GaAs/AlGaAs [3][4][5].The many-body formalism including Feynman diagram technique was developed to study the collective properties of three-dimensional (3D) trions in the bulk semiconductors [6]. The 3D X + and X − confined in a semiconductor cylindrical quantum dot were investigated using a variational procedure within the effective mass approximation [7]. The 3D trions in bulk semiconductors [8] and two-dimensional trions [9] were studied theoretically. According to these studies, the 2D trions have binding energies that are larger than the trions in the corresponding bulk materials. The 2D excitons and 2D X − in QWs in the presence of 2D electron gas were observed experimentally by optical measurements of an excitonic recombination line on the photoluminescence spectra from the QW [10]. The experiments devoted to the observation of 2D X − in QWs in magnetic field by studying the magneto-optical absorption spectra were performed in Ref. [2]. Besides, the 2D X − in QWs in magnetic fie...

Configuration space method for calculating binding energies of exciton complexes in quasi-1D/2D semiconductors

“…Recently, there has been a considerable interest in studies of optical properties of coupled quantum wells (CQWs). [65][66][67][68][69][70][71][72][73][74][75][76] The CQW semiconductor nanostructure ( Fig. 9) consists of two identical semiconductor quantum wells separated by a thin barrier layer of another semiconductor.…”

“…Very recently, the problem of the trion complex formation in CQWs was studied theoretically in great detail for trions composed of a direct exciton and an electron (or a hole) located in the neighboring quantum well [66] [as sketched in Fig. 9 (a)].…”

Stability of trions in coupled quantum wells modeled by two-dimensional bilayers

“…Although our results pertain directly to the negative trion (X − ), the corresponding properties of the positive trion (X + ) can easily be generated by charge conjugation, i.e., by interchanging m e and m h (or, equivalently, by replacing σ by σ −1 Although biexcitons in coupled quantum wells have been studied extensively, there are relatively few theoretical studies of indirect trions. Kulakovskii and Lozovik 28 and Berman et al 29 study trions consisting of a direct exciton in one layer bound to a charge carrier in a neighboring layer, and make the interesting suggestion that Wigner crystallization of trions could occur. Kovalev and Chaplik 30 investigated the behavior of indirect trions in an out-of-plane magnetic field by treating the interlayer electron-hole Coulomb potential within a harmonic approximation.…”

Magnetic-Field-Induced Wigner Crystallization of Charged Interlayer Excitons in van der Waals Heterostructures

“…Coherent states of highly excited semiconductors have been at the forefront of semiconductor materials research since its inception back in the early sixties [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Nowadays, a new family of ultrathin quasi-2D van der Waals (vdW) materials of controlled thickness (also called transdimensional materials [16,17]), particularly bilayer transition metal dichalcogenide (TMD) heterostructures [18], provide unique opportunities to study such states experimentally.…”