Article
Measurements of quasiparticle tunneling in the υ= 5/2 fractional quantum Hall state
Department of Physics, Massachusetts Institute of Technology, 02139, Cambridge, Massachusetts, USA
Physical review. B, Condensed matter (Impact Factor: 3.66). 04/2012; 85(16). DOI: 10.1103/PhysRevB.85.165321 Fulltext preview
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Article: Thermopower of Quantum Hall States in Corbino Geometry as a Measure of Quasiparticle Entropy
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ABSTRACT: Using the Onsager relation between electric and heat transport coefficients, and considering the very different roles played by the quantum Hall condensate and quasiparticles in transport, we argue that near the center of a quantum Hall plateau thermopower in a Corbino geometry measures {\it "entropy per quasiparticle per quasiparticle charge"}. This relation indicates that thermopower measurement in a Corbino setup is a more direct measure of quasiparticle entropy than in a Hall bar. Treating disorder within the selfconsistent Born approximation, we show through an explicit microscopic calculation that this relation holds on an integer quantum Hall plateau at low temperatures. Applying this to nonAbelian quantum Hall states, we argue that Corbino thermopower at sufficiently low temperature becomes temperatureindependent, and measures the quantum dimension of nonAbelian quasiparticles that determines the topological entropy they carry.  [Show abstract] [Hide abstract]
ABSTRACT: We calculate the dominant excitations for the $k$level ($k\in\mathbb{N}$) ReadRezayi (RR) states and their particlehole conjugates, the anti ReadRezayi ($\bar{\textrm{RR}}$), 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 singleqp and the 2agglomerate, with charge $2e^*_k$, have the same scaling and both dominate, while for $k>4$ the 2agglomerates are dominant. Anyway the dominance of the 2agglomerates can be affected by the presence of environmental renormalizations. For all the $k$level $\bar{\textrm{RR}}$ states the singleqp and the 2agglomerate 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 2agglomerates over the nonAbelian singlequasiparticles in the two models and for any value of $k$. We conclude observing that, according these predictions, the dominance of 2agglomerates, at very low energies for the $\nu=5/2$, can be an interesting indication supporting the validity of the antiPfaffian model in comparison to the Pfaffian.  [Show abstract] [Hide abstract]
ABSTRACT: We propose a general mechanism for the renormalization of the tunnelling exponents in edge states of the fractional quantum Hall effect. Mutual effects of the coupling with outofequilibrium 1/f noise and dissipation are considered for both the Laughlin sequence and the composite co and counterpropagating edge states with Abelian or nonAbelian statistics. For states with counterpropagating modes, we demonstrate the robustness of the proposed mechanism in the socalled disorderdominated phase. Prototypes of these states, such as ν = 2/3 and ν = 5/2, are discussed in detail, and the rich phenomenology induced by the presence of a noisy environment is presented. The proposed mechanism could help justify the strong renormalizations reported in many experimental observations carried out at low temperatures. We show how environmental effects could affect the relevance of the tunnelling excitations, leading to important implications, in particular for the ν = 5/2 case.