Experimental constraints and a possible quantum Hall state at $\nu =5/2$

Several topological orders have been proposed to explain the quantum Hall plateau at $\nu =5/2$. The observation of an upstream neutral mode on the sample edge supports the non-Abelian anti-Pfaffian state. On the other hand, tunneling experiments favor the Halperin 331 state which exhibits no upstream modes. No proposed ground states agree with both types of experiments. We find a topological order, compatible with the results of both experiments. That order allows both finite and zero spin polarizations. It is Abelian but its signatures in Aharonov-Bohm interferometry can be similar to those of the Pfaffian and anti-Pfaffian states.

Figure 1

Density profile of a 2D electron gas in a magnetic field. The density is constant in narrow incompressible strips.

Figure 2

Aharonov-Bohm interferometer. Quasiparticles move along the edges and tunnel between the edges at the quantum point contacts QPC1 and QPC2. Several quasiparticles are localized between the edges.