Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2011-11-21
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
11 pages, 5 figures
Scientific paper
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.
Berman Oleg L.
Kezerashvili Roman Ya.
Tsiklauri Shalva M.
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