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:0906.0327 · Physical Review B

Odd-even crossover in a non-Abelian ν=5/2 interferometer

Waheb Bishara, Chetan Nayak

Published Oct 5, 2009• 32 citations
arXivHTMLPDF

Abstract

We compute the backscattered current in a double point-contact geometry of a quantum-Hall system at filling fraction as a function of bias voltage in the weak backscattering regime. We assume that the system is in the universality class of either the Pfaffian or anti-Pfaffian state. When the number of charge quasiparticles in the interferometer is odd, there is no interference pattern. However, the coupling between a charge quasiparticle and the edge causes it to be absorbed by the edge at low energies. Consequently, an interference pattern appears at low bias voltages and temperatures, as if there were an even number of quasiparticles in the interferometer. We relate this problem to that of a semi-infinite Ising model with a boundary magnetic field. Using the methods of perturbed boundary conformal field theory, we give an exact expression for this crossover of the interferometer as a function of bias voltage. Finally, we comment on the possible relevance of our results to recent interference experiments.

DOI
10.1103/physrevb.80.155304

Related papers

Dynamical Disentanglement across a Point Contact in a Non-Abelian Quantum Hall State

Paul Fendley, Matthew P. A. Fisher, Chetan Nayak

We analyze the tunneling of non-Abelian quasiparticles between the edges of a quantum Hall droplet at the Landau level filling fraction nu=5/2, assuming that the electrons in the first excited Landau level organize themselves in the non-Abelian Moore-Read Pfaffian state. By bosonizing the edge theory, we show that an effective spin-1/2 degree of freedom emerges in the description of a point contact. We show how the crossover from the high-temperature regime of weak quasiparticle tunneling between the edges of the droplet, with the 4-terminal Rxx approximately T(-3/2), to the low-temperature limit, with Rxx(-1/10)(h/e2) approximately-T4, is closely related to the two-channel Kondo effect. We give a physical interpretation for the entropy loss of ln(2[square root of 2) in this crossover.

arXiv:cond-mat/0604064•Physical Review Letters•Jul 17, 2006•48 citations

Quasiparticle tunneling in the Moore-Read fractional quantum Hall state

Hua Chen, Zi-Xiang Hu, Kun Yang +2 more

In fractional quantum Hall systems, quasiparticles of fractional charge can tunnel between the edges at a quantum point contact. Such tunneling (or backscattering) processes contribute to charge transport and provide information on both the charge and statistics of the quasiparticles involved. Here, we study quasiparticle tunneling in the Moore-Read state, in which quasiparticles of charges $e/4$ (non-Abelian) and $e/2$ (Abelian) may coexist and both contribute to edge transport. On a disk geometry, we calculate the matrix elements for $e/2$ and $e/4$ quasiholes to tunnel through the bulk of the Moore-Read state, in an attempt to understand their relative importance. We find that the tunneling amplitude for charge $e/2$ quasihole is exponentially smaller than that for charge $e/4$ quasihole, and the ratio between them can be (partially) attributed to their charge difference. We find that including long-range Coulomb interaction only has a weak effect on the ratio. We discuss briefly the relevance of these results to recent tunneling and interferometry experiments at filling factor $\ensuremath{\nu}=5/2$.

arXiv:0905.3607•Physical Review B•Dec 3, 2009•17 citations

Fractional quantum Hall effect at ν=5∕2 : Ground states, non-Abelian quasiholes, and edge modes in a microscopic model

Xin Wan, Zi-Xiang Hu, Edward H. Rezayi +1 more

We present a comprehensive numerical study of a microscopic model of the fractional quantum Hall system at filling fraction $\ensuremath{\nu}=5∕2$, based on the disk geometry. Our model includes Coulomb interaction and a semirealistic confining potential. We also mix in a three-body interaction in some cases to help elucidate the physics. We obtain a phase diagram, discuss the conditions under which the ground state can be described by the Moore-Read state, and study its competition with neighboring stripe phases. We also study quasihole excitations and edge excitations in the Moore-Read-like state. From the evolution of the edge spectrum, we obtain the velocities of the charge and neutral edge modes, which turn out to be very different. This separation of velocities is a source of decoherence for a non-Abelian quasihole and/or quasiparticle (with charge $\ifmmode\pm\else\textpm\fi{}e∕4$) when propagating at the edge; using numbers obtained from a specific set of parameters, we estimate the decoherence length to be around $4\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$. This sets an upper bound for the separation of the two point contacts in a double point-contact interferometer, designed to detect the non-Abelian nature of such quasiparticles. We also find a state that is a potential candidate for the recently proposed anti-Pfaffian state. We find the speculated anti-Pfaffian state is favored in weak confinement (smooth edge), while the Moore-Read Pfaffian state is favored in strong confinement (sharp edge).

arXiv:0712.2095•Physical Review B•Apr 10, 2008•109 citations

Quasi-Particle Tunneling in Anti-Pfaffian Quantum Hall State

Toru Ito, Kentaro Nomura, Naokazu Shibata

We study tunneling phenomena at the edge of the anti-Pfaffian quantum Hall state at the filling factor $ν=5/2$. The edge current in a single point-contact is considered. We focus on nonlinear behavior of two-terminal conductance with the increase in negative split-gate voltage. Expecting the appearance of the intermediate conductance plateau we calculate the value of its conductance by using the renormalization group (RG) analysis. Further, we show that non-perturbative quasi-particle tunneling is effectively described as perturbative electron tunneling by the instanton method. The two-terminals conductance is written as a function of the gate voltage. The obtained results enable us to distinguish the anti-Pfaffian state from the Pfaffian state experimentally.

arXiv:1206.2753•Journal of the Physical Society of Japan•Jul 20, 2012•3 citations

Probing quantum Hall edge chirality and the anyonic exchange angle with a three-path interferometer

Eugene V. Sukhorukov

An upstream neutral mode can influence quasiparticle tunneling even when electric charge propagates only downstream. We propose a three-path fractional quantum Hall interferometer that probes this directional structure through the flux dependence of average terminal currents. Interference between direct and two-step tunneling first contributes at cubic order in the tunneling amplitudes of three weak quantum point contacts. In the local theory, equal drain voltages separate the downstream and upstream responses: for a purely downstream tunneling excitation, the cubic fundamental Aharonov-Bohm harmonic vanishes at one drain, while the other remains bright. Averaging measurements with exchanged unequal drain voltages extends this separation to a configuration in which all contacts are biased. It requires independent calibration of the electrostatic phase shift and fixed or known tunneling magnitudes. For a selected Abelian excitation with two-point correlation exponent $0<Δ_{\boldsymbol{\ell}}<1$, the common low-temperature bias power and directional amplitude ratio determine its scaling dimension and principal exchange angle. We also show that a weak static density interaction spanning two tunneling points can activate the dark harmonic without adding an upstream mode. In the high-bias static limit, the first-order Laughlin activated amplitude scales as $E^{2ν-1}$, where $E$ is the source-drain bias energy and $ν$ is the filling factor. In the weak localized single-mode infrared regime, the bright harmonic retains its leading scaling and can serve as a reference in the same device. The calculation assumes one coherent tunneling species and common-temperature edge correlations with unresolved propagation times.

cond-mat.mes-hallCross-listedarXiv:2607.24451•Jul 28, 2026

Nonequilibrium Transport through a Point Contact in the ν=5/2 Non-Abelian Quantum Hall State

Adrian E. Feiguin, Paul Fendley, Matthew P. A. Fisher +1 more

We analyze charge-e/4 quasiparticle tunneling between the edges of a point contact in a non-Abelian model of the nu = 5/2 quantum Hall state in the presence of a finite voltage difference using the time-dependent density-matrix renormalization group method. We confirm that, as the voltage decreases, the system is broken into two pieces. In the limits of small and large voltage, we recover the results expected from perturbation theory about the infrared and ultraviolet fixed points. We test our methods by finding the analogous nonequilibrium current through a point contact at nu = 1/3.

arXiv:0809.1415•Physical Review Letters•Dec 2, 2008•25 citations
We compute the backscattered current in a double point-contact geometry of a quantum-Hall system at filling fraction as a function of bias voltage in the weak backscattering regime. We assume that the system is in the universality class of either the Pfaffian or anti-Pfaffian state. When the number of charge quasiparticles in the interferometer is odd, there is no interference pattern. However, the coupling between a charge quasiparticle and the edge causes it to be absorbed by the edge at low energies. Consequently, an interference pattern appears at low bias voltages and temperatures, as if there were an even number of quasiparticles in the interferometer. We relate this problem to that of a semi-infinite Ising model with a boundary magnetic field. Using the methods of perturbed boundary conformal field theory, we give an exact expression for this crossover of the interferometer as a function of bias voltage. Finally, we comment on the possible relevance of our results to recent interference experiments.
We analyze the tunneling of non-Abelian quasiparticles between the edges of a quantum Hall droplet at the Landau level filling fraction nu=5/2, assuming that the electrons in the first excited Landau level organize themselves in the non-Abelian Moore-Read Pfaffian state. By bosonizing the edge theory, we show that an effective spin-1/2 degree of freedom emerges in the description of a point contact. We show how the crossover from the high-temperature regime of weak quasiparticle tunneling between the edges of the droplet, with the 4-terminal Rxx approximately T(-3/2), to the low-temperature limit, with Rxx(-1/10)(h/e2) approximately-T4, is closely related to the two-channel Kondo effect. We give a physical interpretation for the entropy loss of ln(2[square root of 2) in this crossover.
In fractional quantum Hall systems, quasiparticles of fractional charge can tunnel between the edges at a quantum point contact. Such tunneling (or backscattering) processes contribute to charge transport and provide information on both the charge and statistics of the quasiparticles involved. Here, we study quasiparticle tunneling in the Moore-Read state, in which quasiparticles of charges e/4e/4e/4 (non-Abelian) and e/2e/2e/2 (Abelian) may coexist and both contribute to edge transport. On a disk geometry, we calculate the matrix elements for e/2e/2e/2 and e/4e/4e/4 quasiholes to tunnel through the bulk of the Moore-Read state, in an attempt to understand their relative importance. We find that the tunneling amplitude for charge e/2e/2e/2 quasihole is exponentially smaller than that for charge e/4e/4e/4 quasihole, and the ratio between them can be (partially) attributed to their charge difference. We find that including long-range Coulomb interaction only has a weak effect on the ratio. We discuss briefly the relevance of these results to recent tunneling and interferometry experiments at filling factor $\ensuremath{\nu}=5/2$.
We present a comprehensive numerical study of a microscopic model of the fractional quantum Hall system at filling fraction $\ensuremath{\nu}=5∕2$, based on the disk geometry. Our model includes Coulomb interaction and a semirealistic confining potential. We also mix in a three-body interaction in some cases to help elucidate the physics. We obtain a phase diagram, discuss the conditions under which the ground state can be described by the Moore-Read state, and study its competition with neighboring stripe phases. We also study quasihole excitations and edge excitations in the Moore-Read-like state. From the evolution of the edge spectrum, we obtain the velocities of the charge and neutral edge modes, which turn out to be very different. This separation of velocities is a source of decoherence for a non-Abelian quasihole and/or quasiparticle (with charge $\ifmmode\pm\else\textpm\fi{}e∕4$) when propagating at the edge; using numbers obtained from a specific set of parameters, we estimate the decoherence length to be around $4\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$. This sets an upper bound for the separation of the two point contacts in a double point-contact interferometer, designed to detect the non-Abelian nature of such quasiparticles. We also find a state that is a potential candidate for the recently proposed anti-Pfaffian state. We find the speculated anti-Pfaffian state is favored in weak confinement (smooth edge), while the Moore-Read Pfaffian state is favored in strong confinement (sharp edge).
We study tunneling phenomena at the edge of the anti-Pfaffian quantum Hall state at the filling factor ν=5/2ν=5/2ν=5/2. The edge current in a single point-contact is considered. We focus on nonlinear behavior of two-terminal conductance with the increase in negative split-gate voltage. Expecting the appearance of the intermediate conductance plateau we calculate the value of its conductance by using the renormalization group (RG) analysis. Further, we show that non-perturbative quasi-particle tunneling is effectively described as perturbative electron tunneling by the instanton method. The two-terminals conductance is written as a function of the gate voltage. The obtained results enable us to distinguish the anti-Pfaffian state from the Pfaffian state experimentally.
An upstream neutral mode can influence quasiparticle tunneling even when electric charge propagates only downstream. We propose a three-path fractional quantum Hall interferometer that probes this directional structure through the flux dependence of average terminal currents. Interference between direct and two-step tunneling first contributes at cubic order in the tunneling amplitudes of three weak quantum point contacts. In the local theory, equal drain voltages separate the downstream and upstream responses: for a purely downstream tunneling excitation, the cubic fundamental Aharonov-Bohm harmonic vanishes at one drain, while the other remains bright. Averaging measurements with exchanged unequal drain voltages extends this separation to a configuration in which all contacts are biased. It requires independent calibration of the electrostatic phase shift and fixed or known tunneling magnitudes. For a selected Abelian excitation with two-point correlation exponent 0<Δℓ<10<Δ_{\boldsymbol{\ell}}<10<Δℓ​<1, the common low-temperature bias power and directional amplitude ratio determine its scaling dimension and principal exchange angle. We also show that a weak static density interaction spanning two tunneling points can activate the dark harmonic without adding an upstream mode. In the high-bias static limit, the first-order Laughlin activated amplitude scales as E2ν−1E^{2ν-1}E2ν−1, where EEE is the source-drain bias energy and ννν is the filling factor. In the weak localized single-mode infrared regime, the bright harmonic retains its leading scaling and can serve as a reference in the same device. The calculation assumes one coherent tunneling species and common-temperature edge correlations with unresolved propagation times.
We analyze charge-e/4 quasiparticle tunneling between the edges of a point contact in a non-Abelian model of the nu = 5/2 quantum Hall state in the presence of a finite voltage difference using the time-dependent density-matrix renormalization group method. We confirm that, as the voltage decreases, the system is broken into two pieces. In the limits of small and large voltage, we recover the results expected from perturbation theory about the infrared and ultraviolet fixed points. We test our methods by finding the analogous nonequilibrium current through a point contact at nu = 1/3.