Thermopower and thermoelectric power factor of ${\mathbb{Z}}_k$ parafermion quantum dots

Abstract

Using the conformal field theory approach to the thermoelectric characteristics of fractional quantum Hall states, previously developed in Nucl. Phys. B 894 (2015) 284, we show that the thermoelectric power factor of Coulomb-blockaded islands, realized by point contacts in Fabry--Pérot interferometers in the ${\mathbb{Z}}_k$ parafermion Hall states, could give reliable signatures for distinguishing the topological orders of different quantum Hall states having identical electric properties. For example, while the conductance peak patterns in the Coulomb blockade regime for such states are practically indistinguishable for $v_n\ll v_c$ even at finite temperature, where $v_n$ and $v_c$ are the Fermi velocities of the neutral and charged modes respectively, the power factors ${\mathcal{P}}_T$ of the corresponding states are much more sensitive to the neutral modes. In particular, the smaller $r=v_n/v_c$ the bigger the asymmetries in the power factor which combined with the thermal broadening of the conductance peaks due to the neutral modes' multiplicities could give us the ultimate tool to figure out which of the competing quantum Hall universality classes are indeed realized in the experiments. We give a complete description of the power factor profiles in the ${\mathbb{Z}}_3$ and ${\mathbb{Z}}_4$ parafermion states with arbitrary number of quasiparticles localized in the bulk which could be useful for comparison with the experiments.

27 pages, 12 PDF figures; v2: added two more references and corrected several misprints

References in corpus (11)

• Non-Abelian Anyons and Topological Quantum Computation
• Experimental studies of the fractional quantum Hall effect in the first excited Landau level
• Conformal invariance of chiral edge theories
• Thermopower as a Possible Probe of Non-Abelian Quasiparticle Statistics in Fractional Quantum Hall Liquids
• Implementation of Clifford gates in the Ising-anyon topological quantum computer
• Extracting net current from an upstream neutral mode in the fractional quantum Hall regime
• Thermoelectric probe for neutral edge modes in the fractional quantum Hall regime
• Experimental signatures of non-Abelian statistics in clustered quantum Hall states
• Thermopower of Quantum Hall States in Corbino Geometry as a Measure of Quasiparticle Entropy
• Towards a universal set of topologically protected gates for quantum computation with Pfaffian qubits
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Cited by in corpus (3)

• Parafermions in Moiré Minibands
• Exact modular $S$ matrix for the ${\mathbb{Z}}_k$ parafermion quantum Hall islands and measurement of non-Abelian anyons
• Thermoelectric characteristics of ${\mathbb{Z}}_k$ parafermion Coulomb islands