Spin excitations in quantum hall systems and their effect on nuclear spin relaxation and photoluminescence

Two problems with respect to spin excitations in quantum Hall systems are studied by means of exact numerical diagonalization. The first one is related to the formation of reversed-spin quasielectrons (QER) in a two-dimensional electron gas (2DEG). The single—particle properties of QER’S as well as the pseudopotentials of their interaction with one another and with Laughlin quasielectrons (QE’s) and quasiholes (QH’s) are calculated. Based on the short-range character of the QER—QER and QER—QE repulsion, the partially unpolarized incompressible states at the filling factors 1/ = 14—1 and 1/ = T55 are postulated within Haldane’s hierarchy scheme. To describe photoluminescence, the family of bound h(QER)n states of a valence hole h and n QER’S are predicted in analogy to the found earlier fractionally charged excitons hQEn. The binding energy and optical selection rules for both families are compared. The hQER is found radiative in contrast to the dark hQE, and the h(QER)2 is found nonradiative in contrast to the bright hQEg. The second problem involves the numerical study of the relaxation rates of nuclear spins coupled through the hyperfine interaction to a 2DEG at magnetic fields corresponding to both fractional and integral Landau level fillings 1/. The spectral functions T_1(E) describing the response of the 2DEG to the reversal of an embedded localized spin are calculated. In a (locally) incompressible 1/ = 1 or 31,; state, the finite Coulomb energy of short spin waves, together with the small nuclear Zeeman energy, prevent nuclear spin relaxation even in the limit of vanishing electron Zeeman energy (EZ). However, we find that the nuclear spins can couple to the internal excitations of mobile finite-size skyrmions that appear in the 2DEG at sufficiently low EZ and at V slightly different from 1 or %. The experimentally observed dependence of nuclear spin relaxation rate on E2 and 1/ is explained in terms of the occurrence of skyrmions and anti-skyrmions of various topological charge.