Article

# Measurements of quasiparticle tunneling in the υ= 5/2 fractional quantum Hall state

International Center for Quantum Materials, Peking University, 100871, Beijing, P.R. China; Department of Physics, Massachusetts Institute of Technology, 02139, Cambridge, Massachusetts, USA; Department of Electrical Engineering, Princeton University, 08544, Princeton, New Jersey, USA

Physical review. B, Condensed matter (Impact Factor: 3.77). 04/2012; 85(16). DOI: 10.1103/PhysRevB.85.165321 - [Show abstract] [Hide abstract]

**ABSTRACT:**We discuss the orbital effect of a tilted magnetic field on the quantum Hall effect in parabolic quantum wells. Many-body states realized at the fractional 1/3 and 1/2 filling of the second electronic subband are studied using finite-size exact diagonalization. In both cases, we obtain the phase diagram consisting of a fractional quantum Hall fluid phase that persists for moderate tilts, and eventually undergoes a direct transition to the stripe phase. It is shown that tilting of the field probes the geometrical degree of freedom of fractional quantum Hall fluids, and can be partly related to the effect of band-mass anisotropy.Physical review. B, Condensed matter 06/2013; 87(24). · 3.77 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We calculate the dominant excitations for the $k$-level ($k\in\mathbb{N}$) Read-Rezayi (RR) states and their particle-hole conjugates, the anti Read-Rezayi ($\bar{\textrm{RR}}$), proposed for quantum Hall states. These states are supposed to be build over the second Landau level with total filling factor $\nu=2+\nu^*$ with $\nu^*=k/(k+2)$ for RR and $\nu^*=2/(k+2)$ for $\bar{\textrm{RR}}$. In the $k$-level RR states, based on $\mathbb{Z}_k$ parafermions, the dominant excitations are the fundamental quasiparticles with fractional charge $e^*_k= e/(k + 2)$, with $e$ the electron charge, if $k=2,3$. For k=4 the single-qp and the 2-agglomerate, with charge $2e^*_k$, have the same scaling and both dominate, while for $k>4$ the 2-agglomerates are dominant. Anyway the dominance of the 2-agglomerates can be affected by the presence of environmental renormalizations. For all the $k$-level $\bar{\textrm{RR}}$ states the single-qp and the 2-agglomerate have the same scaling and both dominate. In this case only the presence of environmental renormalizations can make one dominant over the other. We determine the conditions where the environmental renormalizations of the charged and neutral modes make dominant the Abelian 2-agglomerates over the non-Abelian single-quasiparticles in the two models and for any value of $k$. We conclude observing that, according these predictions, the dominance of 2-agglomerates, at very low energies for the $\nu=5/2$, can be an interesting indication supporting the validity of the anti-Pfaffian model in comparison to the Pfaffian.Physica Scripta 07/2012; T. · 1.03 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We have studied the $\nu=5/2$ fractional quantum Hall state in the regime of extremely low densities, for which the Landau level mixing parameter $\kappa$ spans the so far unexplored $2.52<\kappa<2.82$ range. In the vicinity of $\kappa = 2.6$ an unexpectedly large change in the density dependence of the energy gap is observed which is suggestive of a transition in the $\nu=5/2$ state. Origins of such a transition are discussed, including the possibility of a topological phase transition.02/2013;

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