Experimental constraints and a possible quantum Hall state atν=5/2

Abstract

Several topological orders have been proposed to explain the quantum Hall plateau at ν = 5/2. The observation of an upstream neutral mode on the sample edge supports the non-Abelian antiPfaffian 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.Fractional quantum Hall effect (QHE) exhibits remarkably rich phenomenology. More than 70 filling factors have been discovered. Some of them are well understood but many are not. In particular, the nature of the fragile states in the second Landau level remains a puzzle.The quantum Hall plateaus at the filling factors [1] ν = 5/2 and ν = 7/2 are particularly interesting. Almost all known filling factors have odd denominators. Such quantum Hall states can be explained in a natural way within the Haldane-Halperin hierarchy [2] and the composite fermion picture [3]. Even-denominator filling factors require additional ideas. It was argued that electrons form pairs [4] at ν = 5/2, i.e., the 5/2 state is a topological superconductor. Paring implies that the lowest-charge quasiparticles carry one quarter of an electron charge [1,5]. This was indeed observed in several experiments [6][7][8]. At the same time, the nature of pairing remains an open problem.The investigations of the ν = 5/2 QHE liquid have focused on its topological order which is robust to small variations of sample parameters [2]. This led to a striking proposal of non-Abelian statistics [1,5]. In contrast to ordinary fermions, bosons and Abelian anyons, systems of non-Abelian quasiparticles possess numerous degenerate ground states at fixed quasiparticle positions. This may be useful for quantum computing [1]. Theoretically proposed non-Abelian Pfaffian, anti-Pfaffian, SU (2) 2 and anti-SU (2) 2 states have attracted much interest as possible candidates to explain the QHE plateau at ν = 5/2 (for a review of the proposed states see Refs. 9 and 10). At the same time, one can also construct Abelian states with the same filling factor, such as the Halperin 331, K = 8 and anti-331 states [9,10].Most above-mentioned states were invented before experimental information beyond the existence of the 5/2 QHE plateau and the value of its energy gap became available. This made it impossible to select the correct theory of the 5/2-liquid. The last few years have seen considerable accumulation of the new experimental results [6][7][8][11][12][13][14][15][16][17][18][19]. They provide tight constraints on the topological order at ν = 5/2. We argue that all previously proposed ground state wave functions are excluded by those constraints. To explain the 5/2 plateau we propose a different topological order that satisfies the experimental constrai...

Edge mode velocities in the quantum Hall effect from a dc measurement

“…Experiment does not agree with the predicted universality. For some filling factors, such as 5/2 and 8/3, the observed g agrees reasonably well with some of the theoretical proposals for the topological order [9,56]. At other filling factors, such as 1/3 and 7/3, the experimental results for g are considerably higher than its universal theoretical value [9,57].…”

“…The bias drives a tunneling current I through the QPC. This geometry can be used for a test [8] of the theory of the 5/2 state, proposed in [56]. We focus on the weak tunneling regime.…”

Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian

“…Topological orders described by a K matrix K = ( n m m n ) with n < m actually necessitate such factors for thermodynamic stability [64,65]. For ν = 5/2, the 113 state is a plausible candidate that requires stabilization [66]; a possible LLL stabilized wave function is…”

Long-distance entanglement of spin qubits via quantum Hall edge states

“…We consider both Abelian and non-Abelian topological orders proposed to describe this state. The former include the Halperin 331 state [30] and 113 state [31], and the latter include the Moore-Read (Pfaffian) state [32], the anti-Pfaffian state [33,34], and the SU(2) 2 state [35]. The 331 and 113 states can be both spin polarized and unpolarized, just like the ν = 2 3 QH state.…”

“…We study the RKKY interaction mediated solely by the fractional edge state. In the following, we consider several topological orders proposed for the fractional edge state, including Halperin's 331 and 113 states [30,31], the Pfaffian state [32], the anti-Pfaffian state [33,34] and the SU(2) 2 state [35]. Motivated by the experiment [26], we will always assume separation of charged and neutral degrees of freedom in the edge state.…”