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Fractional quantum Hall states at half-integer filling factors have been observed in many systems beyond the $5/2$ and $7/2$ plateaus in GaAs quantum wells. This includes bilayer states in GaAs, several half-integer plateaus in ZnO-based heterostructures, and quantum Hall liquids in graphene. In all cases, Cooper pairing of composite fermions is believed to explain the plateaus. The nature of Cooper pairing and the topological order on those plateaus are hotly debated. Different orders are believed to be present in different systems. This makes it important to understand experimental signatures of all proposed orders. We review the expected experimental signatures for all possible composite-fermion states at half-integer filling. We address Mach-Zehnder interferometry, thermal transport, tunneling experiments, and Fabry-P{e}rot interferometry. For this end, we introduce a uniform description of the topological orders of Kitaevs sixteenfold way in terms of their wave-functions, effective Hamiltonians, and edge theories.
We study the spectral properties of infinite rectangular quantum graphs in the presence of a magnetic field. We study how these properties are affected when three-dimensionality is considered, in particular, the chaological properties. We then establ
Emergence of half-integer filling factor states, such as nu=5/2 and 7/2, is found in quantum dots by using numerical many-electron methods. These states have interesting similarities and differences with their counterstates found in the two-dimension
In this review the physics of Pfaffian paired states, in the context of fractional quantum Hall effect, is discussed using field-theoretical approaches. The Pfaffian states are prime examples of topological ($p$-wave) Cooper pairing and are character
We theoretically study the quantum Hall effect (QHE) in graphene with an ac electric field. Based on the tight-binding model, the structure of the half-integer Hall plateaus at $sigma_{xy} = pm(n + 1/2)4e^2/h$ ($n$ is an integer) gets qualitatively c
The quantum Hall effect, with a Berrys phase of $pi$ is demonstrated here on a single graphene layer grown on the C-face of 4H silicon carbide. The mobility is $sim$ 20,000 cm$^2$/V$cdot$s at 4 K and ~15,000 cm$^2$/V$cdot$s at 300 K despite contamina