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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 characterized by non-Abelian statistics of their quasiparticles. Here we focus on conditions for their realization and competition among them at half-integer filling factors. Using the Dirac composite fermion description, in the presence of a mass term, we study the influence of Landau level mixing in selecting a particular Pfaffian state. While Pfaffian and anti-Pfaffian are selected when Landau level mixing is not strong, and can be taken into account perturbatively, the PH Pfaffian state requires non-perturbative inclusion of at least two Landau levels. Our findings, for small Landau level mixing, are in accordance with numerical investigations in the literature, and call for a non-perturbative approach in the search for PH Pfaffian correlations. We demonstrated that a method based on the Chern-Simons field-theoretical approach can be used to generate characteristic interaction pseudo-potentials for Pfaffian paired states.
We propose ways to create and detect fractionally charged excitations in emph{integer} quantum Hall edge states. The charge fractionalization occurs due to the Coulomb interaction between electrons propagating on different edge channels. The fraction
Protected edge modes are the cornerstone of topological states of matter. The simplest example is provided by the integer quantum Hall state at Landau level filling unity, which should feature a single chiral mode carrying electronic excitations. In
We report the observation of the quantized Hall effect in suspended graphene probed with a two-terminal lead geometry. The failure of earlier Hall-bar measurements is discussed and attributed to the placement of voltage probes in mesoscopic samples.
The interplay between interaction and disorder-induced localization is of fundamental interest. This article addresses localization physics in the fractional quantum Hall state, where both interaction and disorder have nonperturbative consequences. W
When a gas of electrons is confined to two dimensions, application of a strong magnetic field may lead to startling phenomena such as emergence of electron pairing. According to a theory this manifests itself as appearance of the fractional quantum H