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arXiv:1406.6177 · Nuclear Physics B

Thermoelectric properties of Coulomb-blockaded fractional quantum Hall islands

Lachezar S. Georgiev

Published Mar 12, 2015• 6 citations
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Abstract

We show that it is possible and rather efficient to compute at non-zero temperature the thermoelectric characteristics of Coulomb blockaded fractional quantum Hall islands, formed by two quantum point contacts inside of a Fabry–Pérot interferometer, using the conformal field theory partition functions for the chiral edge excitations. The oscillations of the thermopower with the variation of the gate voltage as well as the corresponding figure-of-merit and power factors, provide finer spectroscopic tools which are sensitive to the neutral multiplicities in the partition functions and could be used to distinguish experimentally between different universality classes sharing the same electric properties. We also propose a procedure for measuring the ratio r=vn/vc of the Fermi velocities of the neutral and charged edge modes for filling factor νH=5/2 from the power-factor data in the low-temperature limit.

DOI
10.1016/j.nuclphysb.2015.02.019

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Thermoelectric characteristics of Zk{\mathbb Z}_kZk​ parafermion Coulomb islands
Using the explicit rational conformal field theory partition functions for the Zk{\mathbb Z}_kZk​ parafermion quantum Hall states on a disk we compute numerically the thermoelectric power factor for Coulomb-blockaded islands at finite temperature. We demonstrate that the power factor is rather sensitive to the neutral degrees of freedom and could eventually be used to distinguish experimentally between different quantum Hall states having identical electric properties. This might help us to confirm whether non-Abelian quasiparticles, such as the Fibonacci anyons, are indeed present in the experimentally observed quantum Hall states.
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We study the thermoelectric transport properties of fractional quantum Hall systems based on an exact diagonalization calculation. Based on the relation between the thermoelectric response and thermal entropy, we demonstrate that thermoelectric Hall conductivity ${\ensuremath{\alpha}}_{xy}$ has power-law scaling ${\ensuremath{\alpha}}_{xy}\ensuremath{\propto}{T}^{\ensuremath{\eta}}$ for gapless composite Fermi-liquid states at filling numbers $\ensuremath{\nu}=1/2$ and 1/41/41/4 at low temperatures (TTT), with an exponent $\ensuremath{\eta}\ensuremath{\sim}0.5$ distinctly different from Fermi liquids. The power-law scaling remains unchanged for different forms of interaction including Coulomb and short-range ones, demonstrating the robustness of non-Fermi-liquid behavior of these interacting systems at low TTT. In contrast, for the 1/31/31/3 fractional quantum Hall state, ${\ensuremath{\alpha}}_{xy}$ vanishes at low TTT with an activation gap associated with neutral collective modes rather than charged quasiparticles. Our results establish another manifestation of the non-Fermi-liquid nature of quantum Hall fluids at a finite temperature.
The surprisingly rich physics of a single Coulomb-blockaded metallic island, when coupled to quantum Hall edge channels, is now well established -- giving rise to charge fractionalization and multi-channel quantum impurity behavior. Here, we show that qualitatively new physics emerges in arrays of such elements. We consider a 1D chain of NNN metallic islands, focusing on thermodynamic signatures such as quantized entropy and anomalous thermal conductance. Universal and robust behavior emerges for energy scales smaller than the charging energy of the islands. In particular, we demonstrate that for the bulk filling factor of ν=1ν=1ν=1, the islands could support a finite heat flow without temperature difference between them. Upon pinching the array with a quantum point contact, we predict an entropy change that scales with the number of islands as ΔS=12kBlog⁡(N+1)ΔS = \frac{1}{2}k_B \log (N+1)ΔS=21​kB​log(N+1), which can be measured using charge detection. This fractional entropy suggests the emergence of a novel type of excitations in the array.
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We study a quantum point contact in the fractional quantum Hall regime at Landau level filling factors $\ensuremath{\nu}=1/3$ and 5/25/25/2. By using exact diagonalizations in the cylinder geometry, we identify the edge modes in the presence of a parabolic confining potential. By changing the sign of the potential, we can access both the tunneling through the bulk of the fluid and the tunneling between spatially separated droplets. This geometry is realized in the quantum point contact geometry for two-dimensional electron gases. In the case of the model Moore-Read Pfaffian state at filling factor $\ensuremath{\nu}=5/2$, we identify the conformal towers of many-body eigenstates including the non-Abelian sector. By a Monte-Carlo technique, we compute the various scaling exponents that characterize the edge modes. In the case of hard-core interactions whose ground states are exact model wave functions, we find equality of neutral and charged velocities, both bosonic and fermionic, for the Pfaffian state.