Effective-field theories for theν=52quantum Hall edge state

Abstract

We present a list of possible effective theories which may describe a QHE edge at filling fraction ν = 5/2. We show that there exist several abelian and non-abelian effective theories (apart from those discussed in the literature) compatible with the physical requirements imposed by the microscopic nature of the system. We compare predictions of these theories with previous proposals and with the results of recent experiments. We identify a set of theories, both abelian and non-abelian, that cannot be distinguished based on the quasihole tunneling data only. We discuss what experimental information may be useful in resolving the ambiguity.PACS numbers: 03.65.Yz, 85.35.Ds One of the most striking predictions of the theory of the fractional quantum Hall effect is that a twodimensional electron gas in a strong magnetic field may exhibit a ground state supporting excitations (quasiparticles) with non-abelian braid statistics. In particular, Wen [1] and Moore and Read [2] have brought forward arguments attempting to explain the ν = 5/2 conductance plateau as a manifestation of such a "nonabelian" state. Not only is this possibility fascinating from the theoretical point of view, it also holds promise for concrete implementations of topologically protected quantum algorithms [3].Among non-abelian quantum Hall states, perhaps the simplest is the Moore-Read (Pfaffian) state, which has a simple intuitive interpretation as a p-wave paired state of composite fermions. The intuitive appeal of the MooreRead state does, however, not give a compelling clue as to its microscopic justification. The Hamiltonian of the many-electron system in a strong magnetic field is not amenable to a well-controlled perturbative treatment, whether in the electron or in the composite-fermion basis. Exact diagonalization numerical studies do not allow one to make fully reliable statements about macroscopically large systems. In this situation the decisive word about the nature of the ν = 5/2 state must come from experiments. A natural target for experimental investigations is the edge of an incompressible quantum Hall fluid supporting gapless excitations, including electric currents, and fractionally charged quasi-holes.In a recent experiment [4], properties of the ν = 5/2 state were investigated by means of a transport measurement in a quantum Hall sample with a narrow constriction. The parameters of the constriction were tuned in such a way that it served as a weak link between two ν = 5/2 quantum Hall edges. The electrical conductance of the constriction exhibits a zero bias peak, whose scaling with temperature is consistent with the assumption that the current is due to weak tunneling of fractionally charged quasi-particles. By fitting the shape of the zero-bias conductance peak to the predictions of a model-independent theory [6] at five different temperatures the experimentalists produced a two-parameter confidence map for the electric charge e * and the scaling dimension, g, of the most relevant (in the renormalization group sense) qua...

Quasiparticle agglomerates and environmental effects in the fractional quantum Hall edge states at ν = 5/2

“…Here, we limit the analysis to the two most popular non-Abelian model, i.e. Pf and aPf in the disorder dominated phase, even if we are aware of other competing proposals [16,34].…”

“…At the same time, the observed even denominator at ν = 5/2 has been interpreted in terms of a p-wave superconducting composite fermion condensate described by the non-Abelian Moore-Read state [7,8,9,10,11]. This state was also analyzed in terms of other topological orders, both purely Abelian [12,13,14] or non-Abelian [15,16]. There is a lot of interest in identifying which model better describes the system having the perspective of topological quantum computation applications [17].…”

Scaling dimension of quantum Hall quasiparticles from tunneling-current noise measurements

“…This can be seen, for example, from the theoretical study of Ref. [5], relating to the ν = 5/2 state.…”

“…However, for a given filling factor ν there may exist several candidate theories predicting the same value of the Hall conductance, but possessing different excitation spectra (e.g., they may differ by whether non-Abelian quasiparticles are present or by the number of transport channels). Probably, the most studied example of such a variety of models is the much debated ν = 5/2 state [3][4][5], first observed in the distant 1987 [6]. In such a situation, the foremost task in the investigation of the FQHE state is to discriminate between the candidate theories.…”

Spectral noise for edge states at the filling factorν= 5/2

“…Among them, the ν = 5/2 state [3] has recently attracted increasing attention in view of its promising application in topologically protected quantum computation [4]. Several models were proposed in order to describe this peculiar state [5] ranging from Abelian models, already considered for other states [6,7], to more exotic non-Abelian descriptions such as the Pfaffian model [8,9] and its particle-hole conjugate, the anti-Pfaffian one [10][11][12]. Despite the different statistical predictions [13], all these models have the common prediction of a fundamental excitation with charge e/4 (e the electron charge), the single-quasiparticle (qp).…”