Quasi-Particle Properties from Tunneling in the v = 5/2 Fractional Quantum Hall State

Abstract

Quasi-particles with fractional charge and statistics, as well as modified Coulomb interactions, exist in a two-dimensional electron system in the fractional quantum Hall (FQH) regime. Theoretical models of the FQH state at filling fraction v = 5/2 make the further prediction that the wave function can encode the interchange of two quasi-particles, making this state relevant for topological quantum computing. We show that bias-dependent tunneling across a narrow constriction at v = 5/2 exhibits temperature scaling and, from fits to the theoretical scaling form, extract values for the effective charge and the interaction parameter of the quasi-particles. Ranges of values obtained are consistent with those predicted by certain models of the 5/2 state.

Fractional quantum Hall hierarchy and the second Landau level

“…[15][16][17][18][19][20] Recent tunneling shot-noise experiments have confirmed the e / 4 fundamental quasihole charge of the =5/ 2 state expected for the MR state. 21 Further recent evidence from the scaling behavior in dc transport experiments 22 at =5/ 2 best agrees with the particle-hole conjugate of MR. 23,24 Although the remaining observed filling fractions in the second Landau level have odd denominators, numerics indicate that the electron correlations for 7 / 3 Յ Յ 8 / 3 have a non-Laughlin character similar to that of =5/ 2, 25 and so only =14/ 5 is expected to be an Abelian state. Aside from the Abelian hierarchy states, the non-Abelian Read-Rezayi ͑RR͒ k-body clustered states 26 ͑which include MR͒ and their particle-hole conjugates are essentially the only single layer spin-polarized descriptions that have been proposed for these FQH plateaus.…”

“…One can also construct these kinds of hierarchies over the particle-hole conjugate of the MR state, which recent experiments seem to indicate may in fact describe the =5/ 2 plateau. 22 This is exactly the same as taking the particle-hole conjugate of the hierarchy states we have built on the MR state. In particular, particle-hole conjugating the state in Eq.…”

Fractional quantum Hall bilayers at half filling: Tunneling-driven non-Abelian phase

“…Some existing theoretical proposals can be used to identify the corresponding edge physics experimentally 52,63,64 . For example, the quasiparticle tunneling conductance acrossing quantum point contacts allows the extraction of the dimensionless interaction parameter g, which reflects the topological order in the bulk and can be directly compared with the theoretical expectations of g = 1/4 for the MR Pfaffian state and g = 3/8 for the (331) Halperin state 10,13 . Another approach is to probe the edge density fluctuation when the sample is coupled to a nearby quantum dot 64 .…”

“…Among them, the non-Abelian FQH effect is expected to form the substrate for topological quantum computation 7 , thus is of great importance. Albeit vigorous research efforts [8][9][10][11][12][13] , to date convincing experimental evidence of non-Abelian FQH states are still rare, with ν = 5/2 and 12/5 as two prominent examples realized in singlecomponent FQH systems. Compared to single-component systems, multicomponent FQH systems with extra degrees of freedom offer additional tunable parameters and allow the observation of richer quantum phase diagrams [14][15][16][17][18] .…”

Symmetry-protected topological orders for interacting fermions: Fermionic topological nonlinearσmodels and a special group supercohomology theory

“…The topologically ordered phases contain long-range entanglement [9] as revealed by topological entanglement entropy [10,11], and cannot be transformed to product states via local unitary (LU) transformations [12][13][14]. Fractional quantum Hall states [15,16], chiral spin liquids [17,18], Z 2 spin liquids [19][20][21], non-Abelian fractional quantum Hall states [22][23][24][25], etc., are examples of topologically ordered phases. The mathematical foundation of topological orders is closely related to tensor category theory [9,12,26,27] and simple current algebra [22,28].…”