Possible Anti-Pfaffian Pairing of Composite Fermions at $\nu =3/8$

We predict that an incompressible fractional quantum Hall state is likely to form at $\nu =3/8$ as a result of a chiral $p$-wave pairing of fully spin polarized composite fermions carrying four quantized vortices, and that the pairing is of the anti-Pfaffian kind. Experimental ramifications include quasiparticles with non-Abelian braid statistics and upstream neutral edge modes.

Figure 1

Exact Coulomb spectra (dashes) at $[N,2Q]=[12,29]$ and [14,33], which correspond to APf and Pf fluxes at $3/8$. Spectra obtained from composite fermion diagonalization are also shown (circles). The energies here and in Fig. 2 are the total Coulomb energies, which do not include the neutralizing background. The dimensions of the Hilbert space in the individual $L$ sectors are shown at the top and the bottom.

Figure 2

Energy spectra obtained from CF diagonalization at both Pf flux (left-hand panels) and APf flux (right-hand panels) at $\nu =3/8$, with $N$ and $2Q$ values shown on the figure. To avoid clutter, the typical estimated statistical uncertainty from Metropolis Monte Carlo evaluation of integrals is shown only on one point. Only states below certain energy are shown.