Direct Observation of Composite Fermions and Their Fully-Spin-Polarized Fermi Sea near $\nu =5/2$

The enigmatic even-denominator fractional quantum Hall state at Landau level filling factor $\nu =5/2$ is arguably the most promising candidate for harboring Majorana quasiparticles with non-Abelian statistics and, thus, of potential use for topological quantum computing. The theoretical description of the $\nu =5/2$ state is generally believed to involve a topological $p$-wave pairing of fully-spin-polarized composite fermions through their condensation into a non-Abelian Moore-Read Pfaffian state. There is, however, no direct and conclusive experimental evidence for the existence of composite fermions near $\nu =5/2$ or for an underlying fully-spin-polarized Fermi sea. Here, we report the observation of composite fermions very near $\nu =5/2$ through geometric resonance measurements and find that the measured Fermi wave vector provides direct demonstration of a Fermi sea with full spin polarization. This lends crucial credence to the model of $5/2$ fractional quantum Hall effect as a topological $p$-wave paired state of composite fermions.

Figure 1

GR features for CFs near $\nu =5/2$. (a) Lateral surface superlattice, inducing a periodic density perturbation in the 2DES. When the cyclotron orbit of the CFs become commensurate with the period of the perturbation, the $i=1$ GR occurs (see text). (b) Magnetoresistance trace for the first-excited LL revealing the $i=1$ CF GR features, resistance minima marked with black arrows flanking $\nu =5/2$. These minima do not coincide with any of the expected FQHE minima which are labeled by blue markers. Blue horizontal lines mark the expected quantized values of the Hall plateau for $\nu =5/2$ and $7/3$ in the ${\rho }_{xy}$ trace. Red arrows indicate the expected positions for the $i=1$ GR for fully-spin-polarized CFs near $\nu =5/2$.

Figure 2

Dependence of the GR features of CFs near (a) $\nu =5/2$ and (b) $\nu =1/2$ on the period of the surface superlattice. Magnetoresistance traces are vertically offset for clarity and the zero-resistance positions are indicated with blue horizontal marks. The expected positions for GRs are marked with red lines. (c) Summary of the positions of the observed GR minima (symbols) and expected values (lines) near $\nu =5/2$.

Figure 3

Evolution of the GR of CFs near $\nu =5/2$ with temperature. Clear GR minima are observed at 30 mK, accompanied by a strong FQHE state at $\nu =5/2$. As the temperature is raised, the GR minima, together with the $V$-shaped minimum at $\nu =5/2$ progressively become weaker and disappear completely at 300 mK.