Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0311339 · Physical Review B

Chiral persistent currents and magnetic susceptibilities in the parafermion quantum Hall states in the second Landau level with Aharonov-Bohm flux

Lachezar S. Georgiev

Published Feb 13, 2004• 7 citations
arXivHTMLPDF

Abstract

Using the effective conformal field theory for the quantum Hall edge states we propose a compact and convenient scheme for the computation of the periods, amplitudes, and temperature behavior of the chiral persistent currents and the magnetic susceptibilities in the mesoscopic disk version of the ${Z}_{k}$ parafermion quantum Hall states in the second Landau level. Our numerical calculations show that the persistent currents are periodic in the Aharonov--Bohm flux with period exactly one flux quantum and have a diamagnetic nature. In the high-temperature regime their amplitudes decay exponentially with increasing the temperature and the corresponding exponents are universal characteristics of non-Fermi liquids. Our theoretical results for these exponents are in perfect agreement with those extracted from the numerical data and demonstrate that there is in general a nontrivial contribution coming from the neutral sector. We emphasize the crucial role of the nonholomorphic factors, first proposed by Cappelli and Zemba in the context of the conformal field theory partition functions for the quantum Hall states, which ensure the invariance of the annulus partition function under the Laughlin spectral flow.

DOI
10.1103/physrevb.69.085305

Related papers

Conformal field theory description of mesoscopic phenomena in the fractional quantum Hall effect

Lachezar S. Georgiev

We give a universal description of the mesoscopic effects occurring in fractional quantum Hall disks due to the Aharonov-Bohm flux threading the system. The analysis is based on the exact treatment of the flux within the conformal field theory framework and is relevant for all fractional quantum Hall states whose edge states CFTs are known. As an example we apply this scheme for the parafermion Hall states and extract the main characteristics of the low- and high- temperature asymptotic behavior of the persistent currents.

arXiv:hep-th/0601075•Jan 12, 2006•0 citations

Pairing Effects at the Edge of Paired Quantum Hall States

Kazusumi Ino

We study pairing effects at the edge of paired fractional quantum Hall states using persistent edge currents as a probe. We give the grand partition functions for edge excitations of paired states (Haldane-Rezayi, Pfaffian, 331) coupled to an Aharanov-Bohm flux and derive the exact formulas of the persistent edge currents. At low temperatures, they exhibit anomalous oscillations in their flux dependence. They converge to the sawtooth function with period ${\ensuremath{\varphi}}_{0}/2$ at zero temperature, which indicates pair condensation. This phenomenon provides an interesting bridge between superconductivity in $2+1$ dimensions and superconductivity in $1+1$ dimensions.

arXiv:cond-mat/9803337•Physical Review Letters•Aug 1, 1998•14 citations

Thermoelectric characteristics of ${\mathbb Z}_k$ parafermion Coulomb islands

Lachezar S. Georgiev

Using the explicit rational conformal field theory partition functions for the ${\mathbb Z}_k$ 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.

arXiv:1601.07034•Jan 26, 2016•0 citations

Partition functions of non-Abelian quantum Hall states

Andrea Cappelli A, Giovanni Viola

Partition functions of edge excitations are obtained for non-Abelian Hall states in the second Landau level, such as the anti-Read–Rezayi state, the Bonderson–Slingerland hierarchy and the Wen non-Abelian fluid, as well as for the non-Abelian spin-singlet state. The derivation is straightforward and unique starting from the non-Abelian conformal field theory data and solving the modular invariance conditions. The partition functions provide a complete account of the excitation spectrum and are used to describe experiments of Coulomb blockade and thermopower.

arXiv:1007.1732•Journal of Physics A Mathematical and Theoretical•Jan 20, 2011•22 citations

Thermoelectric properties of Coulomb-blockaded fractional quantum Hall islands

Lachezar S. Georgiev

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.

arXiv:1406.6177•Nuclear Physics B•Mar 12, 2015•6 citations

Mesoscopic Luttinger liquid theory in an Aharonov-Bohm ring

Mun Dae Kim, Sam Young Cho, Chul Koo Kim +1 more

A careful study on the mesoscopic persistent current in a Luttinger liquid ring is carried out. It is shown that discreteness plays an important role in calculating the persistent current caused by the magnetic flux. At zero temperature, the current is shown to be independent of the interaction even when ${g=(g}_{2}\ensuremath{-}{g}_{4})/2$ is not zero. The current becomes enhanced at finite temperatures with respect to the noninteracting case, when the parameter g is positive.

arXiv:cond-mat/0111102•Physical review. B, Condensed matter•Nov 20, 2002•4 citations
Using the effective conformal field theory for the quantum Hall edge states we propose a compact and convenient scheme for the computation of the periods, amplitudes, and temperature behavior of the chiral persistent currents and the magnetic susceptibilities in the mesoscopic disk version of the Zk{Z}_{k}Zk​ parafermion quantum Hall states in the second Landau level. Our numerical calculations show that the persistent currents are periodic in the Aharonov--Bohm flux with period exactly one flux quantum and have a diamagnetic nature. In the high-temperature regime their amplitudes decay exponentially with increasing the temperature and the corresponding exponents are universal characteristics of non-Fermi liquids. Our theoretical results for these exponents are in perfect agreement with those extracted from the numerical data and demonstrate that there is in general a nontrivial contribution coming from the neutral sector. We emphasize the crucial role of the nonholomorphic factors, first proposed by Cappelli and Zemba in the context of the conformal field theory partition functions for the quantum Hall states, which ensure the invariance of the annulus partition function under the Laughlin spectral flow.
We give a universal description of the mesoscopic effects occurring in fractional quantum Hall disks due to the Aharonov-Bohm flux threading the system. The analysis is based on the exact treatment of the flux within the conformal field theory framework and is relevant for all fractional quantum Hall states whose edge states CFTs are known. As an example we apply this scheme for the parafermion Hall states and extract the main characteristics of the low- and high- temperature asymptotic behavior of the persistent currents.
We study pairing effects at the edge of paired fractional quantum Hall states using persistent edge currents as a probe. We give the grand partition functions for edge excitations of paired states (Haldane-Rezayi, Pfaffian, 331) coupled to an Aharanov-Bohm flux and derive the exact formulas of the persistent edge currents. At low temperatures, they exhibit anomalous oscillations in their flux dependence. They converge to the sawtooth function with period ${\ensuremath{\varphi}}_{0}/2$ at zero temperature, which indicates pair condensation. This phenomenon provides an interesting bridge between superconductivity in 2+12+12+1 dimensions and superconductivity in 1+11+11+1 dimensions.
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.
Partition functions of edge excitations are obtained for non-Abelian Hall states in the second Landau level, such as the anti-Read–Rezayi state, the Bonderson–Slingerland hierarchy and the Wen non-Abelian fluid, as well as for the non-Abelian spin-singlet state. The derivation is straightforward and unique starting from the non-Abelian conformal field theory data and solving the modular invariance conditions. The partition functions provide a complete account of the excitation spectrum and are used to describe experiments of Coulomb blockade and thermopower.
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.