NUMERICAL-STUDIES OF THE PHOTOLUMINESCENCE SPECTRUM OF QUANTUM HALL SYSTEMS

The eigenfunctions and eigenvalues of a system consisting of a finite number of electrons on a two-dimensional plane together with a few holes on a neighboring plane are obtained by numerical diagonalization within the subspace of the lowest Landau level. The energy spectrum and ground state energy per particle are studied as a function of the Landau level degeneracy and the interlayer separation. By evaluating the square of the matrix element of the luminescence operator between the initial state with N(e) electrons and one hole and various final states with N(e) - 1 electrons and no hole, and multiplying by a delta function which conserves energy, the luminescence intensity I(omega) is obtained.