Figure 1: Comparison between theory and experiment.

(a) shows the ground state for the fully polarized state for v≲1/3 with a single composite fermion (CF) hole (empty red circle) in the spin-up lowest ΛL (0↑); (b) shows an additional spin-flip exciton (SFE) that binds with the hole to produce a minimal positively charged fractional skyrmion (FS). (c) shows the state for v≳1/3 with a single CF particle in the spin-down lowest ΛL (0↓), and (d) has an additional SFE. (e) has a CF particle in the spin-up second ΛL (1↑), and (f) has an additional SFE. The composite fermions are shown as particles with two arrows, representing bound vortices, and their up and down spin ΛLs are shown as shaded blue and red rectangles, respectively. In g–i the red dashes (dots) show the exact (CF) energies of the ground states containing a single CF particle or hole (as shown in a,c,e) and the black symbols show the spectrum obtained when an additional SFE is created (as shown in b,d,f). The spherical geometry is used for calculations; panel (g) is for eight particles subjected to 22 flux quanta (a flux quantum is defined as φ₀=hc/e), and (h,i) correspond to 10 particles in 26 flux quanta. (j–l) show the experimentally measured energies of modes below the Zeeman energy. The theoretical energy of the FSs in the dilute limit of ν→1/3 including finite width correction is also shown by blue square. Panels (j,l) are for 50° tilt, whereas (k) is for 30° tilt. All energies in j–l are shown relative to the Zeeman energy, in units of , where is the dielectric constant of the material and is the magnetic length. The modes depicted by red symbols are assigned to fractional skyrmions, green stars in panel k to the excitation shown in Fig. 8d, and the black diamonds and purple stars in panel l to the excitation shown in Fig. 8i. The theoretical error bars arise from the uncertainty in the Monte Carlo calculations and thermodynamic extrapolations, and the experimental error bar reflects the uncertainty in the Lorentzian fits.