Spin excitation spectra of integral and fractional quantum Hall systems

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 $\nu \approx \frac{1}{3},$ 1, 3, and 5. The Hamiltonian matrix of up to $N=14\mathrm{}$ 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 $E_{\mathrm{Z}},$ spin waves (SW’s) and skyrmions are found at $\nu =\frac{1}{3}$ that are composite fermion analogues of the reversed-spin-electron–hole excitations known to occur at $\nu =1.\mathrm{}$ Only for sufficiently large w are stable skyrmions found for $\nu =3\mathrm{}$ 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 $w-E_{\mathrm{Z}}$ 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.