Entanglement entropy and entanglement spectrum of Bi Sb (1 1 1) bilayers.

We study topological properties of Bi Sb bilayers in the (1 1 1) plane using entanglement measures. Electronic structures are investigated within multi-orbital tight-binding model and structural stability is confirmed through first-principles calculations. The topologically non-trivial nature of the bismuth bilayer is proved by the presence of spectral flow in the entanglement spectrum.

Enigmatic 4/11 state: a prototype for unconventional fractional quantum Hall effect.

The origin of the fractional quantum Hall effect (FQHE) at 4/11 and 5/13 has remained controversial. We make a compelling case that the FQHE is possible here for fully spin polarized composite fermions, but with an unconventional underlying physics. Thanks to a rather unusual interaction between composite fermions, the FQHE here results from the suppression of pairs with a relative angular momentum of three rather than one, confirming the exotic mechanism proposed by Wójs, Yi, and Quinn [Phys.

Role of exciton screening in the 7/3 fractional quantum Hall effect.

The excitations of the 7/3 fractional Hall state, one of the most prominent states in the second Landau level, are not understood. We study the effect of screening by composite fermion excitons and find that it causes a strong renormalization at 7/3, thanks to a relatively small exciton gap and a relatively large residual interaction between composite fermions. The excitations of the 7/3 state are to be viewed as composite fermions dressed by a large exciton cloud.

Possible anti-Pfaffian pairing of composite fermions at ν = 3/8.

We predict that an incompressible fractional quantum Hall state is likely to form at ν = 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.

Neutral fermion excitations in the Moore-Read state at filling factor ν = 5/2.

We present evidence supporting the weakly paired Moore-Read phase in the half-filled second Landau level, focusing on some of the qualitative features of its excitations. Based on numerical studies, we show that systems with odd particle number at the flux N(ϕ)=2N-3 can be interpreted as a neutral fermion mode of one unpaired fermion, which is gapped. The mode is found to have two distinct minima, providing a signature that could be observed by photoluminescence.

Global phase diagram of the fractional quantum Hall effect arising from repulsive three-body interactions.

The model of fermions in a magnetic field interacting via a purely three-body repulsive interaction has attracted interest because it produces, in the limit of short range interaction, the Pfaffian state with non-Abelian excitations. We show that this is part of a rich phase diagram containing a host of fractional quantum Hall states, a composite fermion Fermi sea, and a pairing transition. This is entirely unexpected, because the appearance of composite fermions and fractional quantum Hall effect is ordinarily thought to be a result of strong two-body repulsion.

Landau-level mixing and the emergence of Pfaffian excitations for the 5/2 fractional quantum Hall effect.

We report on exact diagonalization studies for fully spin polarized 5/2 fractional quantum Hall effect, incorporating Landau-level mixing through the Bishara-Nayak effective interaction. We find that there is an experimentally accessible region in the phase diagram where the Pfaffian model accurately describes not only the ground state but also the neutral and charged excitations. These results are consistent with the observed persistence of the 5/2 Hall effect down to very low magnetic fields; they are also relevant to the experimental attempts to detect non-Abelian braid statistics.

Skyrmions in the Moore-Read state at nu=5/2.

We study charged excitations of the non-Abelian Moore-Read liquid at a filling factor nu=5/2, allowing for spin depolarization. Using a combination of numerical studies, and taking account of nonzero well widths, we find that at a sufficiently low Zeeman energy it is energetically favorable for charge e/4 quasiholes to bind into Skyrmions of charge e/2. We show that Skyrmion formation is further promoted by disorder, and argue that this can lead to a depolarized nu=5/2 ground state in realistic experimental situations.