Spin excitation spectra of integral and fractional quantum Hall systems - art. no. 045323

摘要

Results are presented of detailed numerical calculations for the spin excitations of a two-dimensional electron gas confined to a quantum well (QW) of finite width w, at magnetic fields corresponding to both fractional and integral Landau level (LL) fillings nuapproximate to1/3, 1, 3, and 5. The Hamiltonian matrix of up to N=14 interacting electrons is diagonalized exactly in Haldane spherical geometry, neglecting excitations to higher orbital LL's or to higher QW subbands. At sufficiently low Zeeman energy E-Z, spin waves (SW's) and skyrmions are found at nu=1/3 that are composite fermion analogues of the reversed-spin-electron-hole excitations known to occur at nu=1. Only for sufficiently large w are stable skyrmions found for nu=3 and 5. Their stability depends upon the interaction pseudopotentials of their constituents. We propose a criterion on the pseudopotential needed for skyrmion stability, and construct phase diagrams (in the w-E-Z plane) for skyrmions of different size. The SW-SW and skyrmion-skyrmion interactions are also discussed, and the noninteracting SW condensates as well as the skyrmion fluids with Laughlin correlations (at intermediate skyrmion densities) are proposed. [References: 79]