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:0704.3291

Double Point Contact in the k=3 Read-Rezayi State

Lukasz Fidkowski

Published Apr 25, 2007• 9 citations
arXivHTMLPDF

Abstract

We compute the dependence of the tunneling current in a double point contact in the k=3 Read-Rezayi state (which is conjectured to describe an incompressible quantum hall fluid at filling fraction nu=12/5) on voltage, separation between the two contacts, and temperature. Using the tunneling hamiltonian of cond-mat/0607431, we show that the effect of quasiholes in the bulk region between the two contacts is simply an overall constant multiplying the interference term. This is the same effect as found for the differential conductivity in cond-mat/0601242; the difference is that we do an actual edge theory calculation and compute the full current-voltage curve at weak tunneling.

DOI
10.48550/arxiv.0704.3291

Related papers

Exact nonequilibrium transport through point contacts in quantum wires and fractional quantum Hall devices

Paul Fendley, A. W. W. Ludwig, Hubert Saleur

We have recently calculated exact nonequilibrium quantum transport properties through a point contact in a Luttinger liquid. Using a particular quasiparticle basis of the Hilbert space dictated by integrability, we here compute explicitly the exact I(V) characteristic and conductance out of equilibrium as a function of driving voltage V and temperature T. These are described by universal scaling functions of two variables, the scaled point-contact interaction strength, and V/T. The differential-conductance curve as a function of the interaction strength broadens significantly as V/T is increased, and develops a pronounced maximum at a (universal) critical value (eV/${\mathit{k}}_{\mathit{B}}$T)=7.188 68. . .. In addition, we derive an exact duality between strong and weak backscattering. The theory presented here has recently been realized experimentally in resonant tunneling-transport experiments between edge states in fractional quantum Hall effect devices. In this context the exact duality is between electron tunneling and Laughlin-quasiparticle tunneling.

arXiv:cond-mat/9503172•Physical review. B, Condensed matter•Sep 15, 1995•289 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

Transport through constricted quantum Hall edge systems: Beyond the quantum point contact

Siddhartha Lal

Motivated by surprises in recent experimental findings, we study transport in a model of a quantum Hall edge system with a gate-voltage controlled constriction. A finite backscattered current at finite edge bias is explained from a Landauer-Buttiker analysis as arising from the splitting of edge current caused by the difference in the filling fractions of the bulk $({\ensuremath{\nu}}_{1})$ and constriction $({\ensuremath{\nu}}_{2})$ quantum Hall fluid regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model. The constriction region splits the incident long-wavelength chiral edge density-wave excitations among the transmitting and reflecting edge states encircling it. The competition between two interedge tunneling processes taking place inside the constriction, related by a quasiparticle-quasihole (qp-qh) symmetry, is accounted for by computing the boundary theories of the system. This competition is found to determine the strong coupling configuration of the system. A separatrix of qp-qh symmetric gapless critical states is found to lie between the relevant renormalization group (RG) flows to a metallic and an insulating configuration of the constriction system. This constitutes an interesting generalization of the Kane-Fisher quantum impurity model. The features of the RG phase diagram are also confirmed by computing various correlators and chiral linear conductances of the system. In this way, our results find excellent agreement with many recent puzzling experimental results for the cases of ${\ensuremath{\nu}}_{1}=1∕3$ and 1. We also discuss and make predictions for the case of a constriction system with ${\ensuremath{\nu}}_{2}=5∕2$.

arXiv:0709.3164•Physical Review B•Jan 29, 2008•9 citations

Randomness at the edge: Theory of quantum Hall transport at filling ν=2/3

C. L. Kane, Matthew P. A. Fisher, Joseph Polchinski

Current Luttinger liquid edge state theories for filling \ensuremath{\nu}=2/3 predict a nonuniversal Hall conductance, in disagreement with experiment. Upon inclusion of random edge tunneling we find a phase transition into a new disorder-dominated edge phase. An exact solution of the random model in this phase gives a quantized Hall conductance of 2/3 and a neutral mode propagating upstream. The presence of the neutral mode changes the predicted temperature dependence for tunneling through a point contact from ${\mathit{T}}^{2/\ensuremath{\nu}\mathrm{\ensuremath{-}}2}$ to ${\mathit{T}}^{2}$.

arXiv:cond-mat/9402108•Physical Review Letters•Jun 27, 1994•316 citations

Many-body study of a quantum point contact in the fractional quantum Hall regime at ν=5/2

Paul Soulé, Th. Jolicœur, P. Lecheminant

We study a quantum point contact in the fractional quantum Hall regime at Landau level filling factors $\ensuremath{\nu}=1/3$ and $5/2$. 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.

arXiv:1307.3362•Physical Review B•Dec 5, 2013•4 citations

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
We compute the dependence of the tunneling current in a double point contact in the k=3 Read-Rezayi state (which is conjectured to describe an incompressible quantum hall fluid at filling fraction nu=12/5) on voltage, separation between the two contacts, and temperature. Using the tunneling hamiltonian of cond-mat/0607431, we show that the effect of quasiholes in the bulk region between the two contacts is simply an overall constant multiplying the interference term. This is the same effect as found for the differential conductivity in cond-mat/0601242; the difference is that we do an actual edge theory calculation and compute the full current-voltage curve at weak tunneling.
We have recently calculated exact nonequilibrium quantum transport properties through a point contact in a Luttinger liquid. Using a particular quasiparticle basis of the Hilbert space dictated by integrability, we here compute explicitly the exact I(V) characteristic and conductance out of equilibrium as a function of driving voltage V and temperature T. These are described by universal scaling functions of two variables, the scaled point-contact interaction strength, and V/T. The differential-conductance curve as a function of the interaction strength broadens significantly as V/T is increased, and develops a pronounced maximum at a (universal) critical value (eV/kB{\mathit{k}}_{\mathit{B}}kB​T)=7.188 68. . .. In addition, we derive an exact duality between strong and weak backscattering. The theory presented here has recently been realized experimentally in resonant tunneling-transport experiments between edge states in fractional quantum Hall effect devices. In this context the exact duality is between electron tunneling and Laughlin-quasiparticle tunneling.
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 $\ensuremath{\nu}=5/2$.
Motivated by surprises in recent experimental findings, we study transport in a model of a quantum Hall edge system with a gate-voltage controlled constriction. A finite backscattered current at finite edge bias is explained from a Landauer-Buttiker analysis as arising from the splitting of edge current caused by the difference in the filling fractions of the bulk $({\ensuremath{\nu}}_{1})$ and constriction $({\ensuremath{\nu}}_{2})$ quantum Hall fluid regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model. The constriction region splits the incident long-wavelength chiral edge density-wave excitations among the transmitting and reflecting edge states encircling it. The competition between two interedge tunneling processes taking place inside the constriction, related by a quasiparticle-quasihole (qp-qh) symmetry, is accounted for by computing the boundary theories of the system. This competition is found to determine the strong coupling configuration of the system. A separatrix of qp-qh symmetric gapless critical states is found to lie between the relevant renormalization group (RG) flows to a metallic and an insulating configuration of the constriction system. This constitutes an interesting generalization of the Kane-Fisher quantum impurity model. The features of the RG phase diagram are also confirmed by computing various correlators and chiral linear conductances of the system. In this way, our results find excellent agreement with many recent puzzling experimental results for the cases of ${\ensuremath{\nu}}_{1}=1∕3$ and 1. We also discuss and make predictions for the case of a constriction system with ${\ensuremath{\nu}}_{2}=5∕2$.
Current Luttinger liquid edge state theories for filling \ensuremath{\nu}=2/3 predict a nonuniversal Hall conductance, in disagreement with experiment. Upon inclusion of random edge tunneling we find a phase transition into a new disorder-dominated edge phase. An exact solution of the random model in this phase gives a quantized Hall conductance of 2/3 and a neutral mode propagating upstream. The presence of the neutral mode changes the predicted temperature dependence for tunneling through a point contact from ${\mathit{T}}^{2/\ensuremath{\nu}\mathrm{\ensuremath{-}}2}$ to T2{\mathit{T}}^{2}T2.
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.
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.