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A selfconsistent many body approach for the description of gases with quartets, trions, and pairs is presented. Applications to 3D Fermi systems at low density are discussed.

We consider a restricted three-body problem, where two interacted particles are located in a 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 (holes) and direct excitons spatially separated in different parallel neighboring quantum wells 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 is 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 wavefunctions of the spatially indirect trion are obtained, their dependencies 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 in the same material.

Effects of geometrical confinement and magnetic field strength on the binding energies of trions (positive trion and negative trion) in a CdTe/ZnTe parabolic dot are investigated. Coulomb interaction energy is obtained by employing Hartree potential and the results are found numerically. The modified Chandrasekhar wavefunctions are employed to obtain the respective energies. The confined energies and the respective binding energies of charged trions are investigated by the self-consistent method. The Poisson equation is used to find the electron and hole potentials. The dielectric mismatch is included throughout the calculations. Magneto-optical transition energies for charged trions in the presence of magnetic field are observed. The effective Landé factor is brought out. Raman shift and the Raman intensity of positive and negative trions for various magnetic field strengths in the CdTe/ZnTe nanostructures are investigated. The dependence of Raman resonance on the magnetic field and the geometrical confinement effect is brought out.

A three-fermion problem in a three-dimensional lattice with anisotropic hopping is solved by discretizing the Schrödinger equation in momentum space. Interparticle interaction comprises on-site Hubbard repulsion and in-plane nearest-neighbor attraction. By comparing the energy of three-fermion bound clusters (trions) with the energy of one pair plus one free particle, a trion formation threshold is accurately determined, and the region of pair stability is mapped out. It is found that the “close-packed” density of fermion pairs, which is associated with a maximum pair condensation temperature in this model, is the highest in a strongly anisotropic case. It is also argued that pair superconductivity with the highest critical temperature is always close to trion formation, which makes the system prone to phase separation and local charge ordering.

Time-resolved and time-integrated circularly-polarized photoluminescence of excitons and trions have been studied in external magnetic fields up to 10 T. ZnSe-based quantum well structures of n-type with carrier densities varied from 5×10⁹ to 10¹¹cm^-2 were used in this study. Absence of the chemical equilibrium in the exciton–trion system has been demonstrated at low temperatures (<10 K). The recovery of the equilibrium has been found at elevated temperatures (<15 K).

Results of experimental studies of photoluminescence (PL) and PL excitation (PLE) spectra of MBE grown single quantum wells (QWs) formed by insertion of few CdSe monolayers in the ZnSe matrix are reviewed. PL spectra of such quantum objects originate from the luminescence of CdSe-rich nanoislands. Two types of island emitting states, namely ground and metastable ones, contribute to the low- and high-energy parts of the PL band, respectively. An interplay between these contributions is responsible for the anomalous temperature dependence of the maximum position of the PL band. The optical orientation and optical alignment experiments at resonant excitations allow to elucidate the nature of the two types of the emitting states. PLE spectra of ground and metastable states have strongly differing characters at excitation below some characteristic energy E_ME which is identified as the exciton percolation threshold. A theoretical model of the absorption spectra of emitting island states is presented, and practical applications of the model for the characterization of the island lateral concentration profiles are reported.