Figure 1

(Color online) Two possible ground states at the integer filling factor $\nu =2$, (a) polarized and (b) spin-singlet one, and the lowest excitations in the noninteracting electron picture with and without spin flip.Reuse & Permissions

Figure 2

Schematics of dispersion branches of the lowest excitations from the (a) polarized, (b) spin-singlet ground states corresponding to the CF filling factor ${\nu }^{\ast }=2$ (i.e., $\nu =2/5$ and $\nu =2/3$). Solid (dashed) lines show no-spin-flip (single-spin-flip) excitations. The line $\left(\alpha \right)$ is based on our earlier data (Ref. 24) and all other sketches on the ED data detailed in Appendix . Employing diverse approaches, some of the dispersions have already been estimated before: $\left(\alpha \right)$ (Ref. 25), $\left(\beta \right)$ (Ref. 26), and $\left(\gamma \right)$ (Ref. 13).Reuse & Permissions

Figure 3

(Color online) A special class of low-energy states in a fully polarized $\nu =2$ system plus (a) one QEr and (b) one QH. We use these sketches in the CF sense to visualize the lowest-energy states with various total spin in $\nu =2/5$ or 2/3 plus one QEr or QH.Reuse & Permissions

Figure 4

(Color online) Above: Excitation energies in an ideal disorder-free system based on the QE/QH mode energy of Table and spin-flip energies of Table . Total number of spin flips involved is given in parentheses. Below: Fields corresponding to the spin transitions in the lowest excited state. Corresponding Coulomb energies of the excitations and total number of spin flips are given on the right. QH/QE/QEr denotes a quasihole/quasielectron/quasielectron with reversed spin, and if any of the objects involves more spin flips, it is indicated by the subscript. Larger scale numerical calculations are needed to find out whether excitations with more spin flips may occur (in range denoted by “?”).Reuse & Permissions

Figure 5

(Color online) Experimental transport activation gaps from Ref. 33 with fits assuming 0,1,2, or 3 spin flips (for $\nu =2/3$) and 0 or 1 spin flip (for $\nu =2/5$). Corresponding fit parameters of Eq. (5) are summarized in Table .Reuse & Permissions

Figure 6

(Color online) ED data for the $S_z=N_e/2$ subspace of $\nu =2/5$ with $N_e=8$, 10, and 12 electrons on torus (left panel) and sphere [right panel; $2Q$ used was 16, 21, and 26, corresponding to the topological shift (Ref. 37) $\gamma =-4$]. The sketch of the no-spin-flip mode dispersion in Fig. 2a was drawn using the torus data (thick solid line). CF calculation in spherical geometry is shown for comparison on the right by a thin solid line (taken from Fig. 1 of Ref. 27).Reuse & Permissions

Figure 7

(Color online) ED data for the $S_z=N_e/2-1$ subspace of (a) $\nu =2/5$ with $N_e=8$ electrons and (b) $\nu =2/3$ with $N_e=10$ and 12 electrons. Differences between the torus and spherical geometry results are smaller than in Fig. 6, so that all data could be reasonably plotted in one viewgraph. The dashed lines were taken over to the sketches in Fig. 2a. Values of $2Q$ used were 16 (left) and 15 (right).Reuse & Permissions

Figure 8

(Color online) ED data for (a) the $S_z=0$ and (b) the $S_z=1$ subspaces of $\nu =2/5$ with $N_e=8$ electrons. Torus and spherical geometry results are again plotted together in one viewgraph. The solid and dashed lines are replotted on the upper panel of Fig. 2b. Values of $2Q$ used were 17 for all spherical geometry calculations in this figure.Reuse & Permissions

Figure 9

(Color online) Same as Fig. 8 for $\nu =2/3$ and $N_e=10$ electrons (and $2Q=14$). Solid and dashed lines are replotted on the lower panel of Fig. 2b.Reuse & Permissions

Figure 10

(Color online) ED data for the $\nu =2/5$ polarized ground state plus one extra (a) quasielectron and (b) quasihole. The data points are connected by lines just for sake of better readability of the graph. Single-particle sketches in terms of noninteracting composite fermions illustrate the interpretation of the angular momenta of the low-energy states (given in text). Gray-filled points represent the background (incompressible ground state) particles, filled and empty points denote the excess particles, quasielectrons and quasiholes.Reuse & Permissions

Figure 11

(Color online) ED data for the $\nu =2/3$ polarized ground state plus one extra QE and QH.Reuse & Permissions

Figure 12

(Color online) The same as Fig. 10 for the $\nu =2/5$ spin-singlet ground state.Reuse & Permissions

Figure 13

(Color online) The same as Fig. 11 for the $\nu =2/3$ spin-singlet ground state.Reuse & Permissions

Figure 14

(Color online) Profiles of charge densities of different quasiparticles at $\nu =1/3$ and 2/5.Reuse & Permissions