Figure 1

Density profiles for some type-1 and type-2 CF crystals on the surface of a sphere. All systems contain $N=96$ particles. The parameters are (a) MZ crystal and (b) type-1 ${}^2\mathrm{CFC}$ for $2Q=433$ at $\nu =0.2188$, (c) type-2 ${}^4\mathrm{CFC}$ for $N_c=42$ and $2Q=433$ at $\nu =0.2188$, (d) type-2 ${}^4\mathrm{CFC}$ for $N_c=24$ and $2Q=451$ at $\nu =0.2103$. The filling factor in this region is determined using the interpolation relation $\nu =(N+2)/(2Q+15)$, which correctly reproduces the known finite size “shifts” in $2Q$ at $\nu =1/5$ and $\nu =2/9$. The density is plotted in units of ${\rho }_0=N/4\pi R^2$. While comparing different plots, note that the radius of the sphere is $R=\sqrt{Q}$ in units of the magnetic length.Reuse & Permissions

Figure 2

Upper panels: Energy per particle as a function of filling factor for various type-1 and type-2 CFC states. The latter are labeled FQHE. All energies are quoted relative to a reference energy $E_{\mathrm{fit}}=-0.782133{\nu }^{1/2}+0.2623{\nu }^{3/2}+0.18{\nu }^{5/2}-15.1e^{-2.07/\nu }$, which has a form similar to that in Ref. 14 but with coefficients modified to display the energy differences between the competing states more clearly. Lower panels: Shear moduli of type-1 crystals of composite fermions with $2p$ vortices. The shear modulus of the MZ crystal, given by the solid black line, is shown for reference. The shear modulus of the ${}^{2p}\mathrm{CFC}$ is indicated by a solid line in the regime where it is the ground state and by a dashed line otherwise. The regions $0<\nu <1/6$ and $1/6<\nu <4/17$ are shown in separate panels because different filling factor scales are used for them.Reuse & Permissions

Figure 3

Melting temperature of the CF crystal at $\nu =1/7$ and $\nu =0.213$ as determined by the Kosterlitz-Thouless mechanism (solid lines) and a first order transition into a FQHE liquid [46] (dotted lines). The inset shows the phase diagram in the filling factor range $1/5\le \nu \le 2/9$ for $B=25\mathrm{T}$.Reuse & Permissions