We carry out microphotoluminescence measurements of an acceptor-bound exciton (A^0X) recombination in the applied magnetic field with a single impurity resolution. In order to describe the obtained spectra we develop a theoretical model taking into account a quantum well (QW) confinement, an electron-hole and hole-hole exchange interaction. By means of fitting the measured data with the model we are able to study the fine structure of individual acceptors inside the QW. The good agreement between our experiments and the model indicates that we observe single acceptors in a pure two-dimensional environment whose states are unstrained in the QW plain.
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