We study the trion and biexciton in transition metal dichalcogenides monolayers within the framework of a nonrelativistic potential model using the method of hyperspherical harmonics (HH). We solve the three- and four-body Schr\"odinger equations with the Keldysh potential by expanding the wave functions of a trion and biexciton in terms of the antisymmetrized HH. Results of the calculations for the ground state energies are in good agreement with similar calculations for the Keldysh potential and in reasonable agreement with experimental measurements of trion and biexciton binding energies.Comment: 4 page
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...
Abstract. The three-body kaonic system KK _ K is studied in the framework of a singlechannel potential nonrelativistic model using the method of hyperspherical harmonics in momentum representation. Calculations are performed with two sets of KK and K _ K potentials. A quasibound state for the KK _ K system with spin-parity 0 − and isospin 1/2 is found below the three-kaon threshold.Recently, there has been special interest in few-body systems constituted of two or more kaons. Particularly noteworthy is the possibility of formation of quasibound states in a KK _ K system. We study the KK _ K system using a nonrelativistic potential model within the framework of the hyperspherical harmonics (HH) method in momentum representation and consider the KK Table 2. A reasonable convergence for the ground state energy is reached for the grand angular momentum 10, and we limit our considerations to this a
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