arXiv:cond-mat/0105286 · Journal of the Physical Society of Japan

Strong Quasi-Particle Tunneling Study in the Paired Quantum Hall States

Kentaro Nomura, D. Yoshioka

Published Dec 15, 2001• 3 citations

Abstract

The quasi-particle tunneling phenomena in the paired fractional quantum Hall states are studied. A single point-contact system is first considered. Because of relevancy of the quasi-particle tunneling term, the strong tunneling regime should be investigated. Using the instanton method it is shown that the strong quasi-particle tunneling regime is described as the weak electron tunneling regime effectively. Expanding to the network model the paired quantum Hall liquid to insulator transition is discussed.

DOI: 10.1143/jpsj.70.3632

Related papers

Tunneling of quasiholes in the fractional quantum Hall regime

Moritz Helias, Daniela Pfannkuche

arXiv:cond-mat/0403126Mar 3, 20040 citations

Quasi-Particle Tunneling in Anti-Pfaffian Quantum Hall State

Toru Ito, Kentaro Nomura, Naokazu Shibata

arXiv:1206.2753Journal of the Physical Society of JapanJul 20, 20123 citations

Universal transport theory for paired fractional quantum Hall states in the quantum point contact geometry

Eslam Ahmed, Ryoi Ohashi, Hiroki Isobe +2 more

arXiv:2601.08792Physical review. B./Physical review. BApr 30, 20261 citation

Zero Mode Tunnelling in a Fractional Quantum Hall Device

Stephanie Jane Huntington, Vadim Cheianov

arXiv:1410.6638Oct 24, 20143 citations

Quasiparticle tunneling in the Moore-Read fractional quantum Hall state

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

arXiv:0905.3607Physical Review BDec 3, 200917 citations

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

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

arXiv:cond-mat/9503172Physical review. B, Condensed matterSep 15, 1995289 citations

arXiv:cond-mat/0105286 · Journal of the Physical Society of Japan

Strong Quasi-Particle Tunneling Study in the Paired Quantum Hall States

Kentaro Nomura, D. Yoshioka

Published Dec 15, 2001• 3 citations

arXiv HTML PDF

Abstract

DOI: 10.1143/jpsj.70.3632

Related papers

Tunneling of quasiholes in the fractional quantum Hall regime

Moritz Helias, Daniela Pfannkuche

The elementary low energy excitations in the fractional quantum Hall (FQH) regime are known to be fractionally charged quasiparticles and quasiholes. This work focusses on quasiholes in a finite system of a few electrons treated by exact numerical diagonalization. Recent experimental [Chung et al., PRB 67, 201104 (2003)] and theoretical [Kane, Fisher, PRB 67, 045307 (2003)] work on quantum point contacts in the FQH regime showed strong evidence for single quasiparticle tunneling to be forbidden at low temperature. We want to gain insight into such constricted FQH systems by a numerical approach. Initially the basics of numerically treating a system in rectangular geometry and procedures to insert a quasihole excitation are presented. The excitations' stability and fractional charge is confirmed for different interactions. The question of quasihole tunneling is approached in two different systems: 1. A system posessing bound, localized states of a quasihole shows evidence for tunnel coupling between these states to exist. 2. Different potential forms to model a quantum point contact are investigated and the injection of a single quasihole near the constriction is surveyed in the system's time evolution.The elementary low energy excitations in the fractional quantum Hall (FQH) regime are known to be fractionally charged quasiparticles and quasiholes. This work focusses on quasiholes in a finite system of a few electrons treated by exact numerical diagonalization. Recent experimental [Chung et al., PRB 67, 201104 (2003)] and theoretical [Kane, Fisher, PRB 67, 045307 (2003)] work on quantum point contacts in the FQH regime showed strong evidence for single quasiparticle tunneling to be forbidden at low temperature. We want to gain insight into such constricted FQH systems by a numerical approach. Initially the basics of numerically treating a system in rectangular geometry and procedures to insert a quasihole excitation are presented. The excitations' stability and fractional charge is confirmed for different interactions. The question of quasihole tunneling is approached in two different systems: 1. A system posessing bound, localized states of a quasihole shows evidence for tunnel coupling between these states to exist. 2. Different potential forms to model a quantum point contact are investigated and the injection of a single quasihole near the constriction is surveyed in the system's time evolution.

arXiv:cond-mat/0403126Mar 3, 20040 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.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:1206.2753Journal of the Physical Society of JapanJul 20, 20123 citations

Universal transport theory for paired fractional quantum Hall states in the quantum point contact geometry

Eslam Ahmed, Ryoi Ohashi, Hiroki Isobe +2 more

Even-denominator fractional quantum Hall (FQH) states can be viewed as topological superconductors of composite fermions, supporting a charged chiral mode and $|\mathcal{C}_{cf}|$ neutral Majorana modes set by the Chern number $\mathcal{C}_{cf}$ . Despite ongoing efforts, distinguishing the many competing paired phases remains an open problem. In this work, we propose a unified theory of charge transport across a quantum point contact (QPC) for general paired FQH states described by an $so(N)_1 \times u(1)$ conformal field theory. We derive the boundary effective action for an arbitrary number of Majorana fermions $N=|\mathcal{C}_{cf}|$ and develop a non-perturbative instanton approximation to describe tunneling processes. We establish a weak-strong duality relating strong quasiparticle tunneling to weak electron tunneling. We calculate the scaling dimensions of the tunneling operators and demonstrate that while the weak-coupling fixed point is generally unstable, the strong-coupling fixed point is stable for physically relevant filling fractions and number of Majorana fermions. These transport exponents provide a distinct experimental fingerprint to identify the topological phases of even-denominator FQH states.Even-denominator fractional quantum Hall (FQH) states can be viewed as topological superconductors of composite fermions, supporting a charged chiral mode and $|\mathcal{C}_{cf}|$ neutral Majorana modes set by the Chern number $\mathcal{C}_{cf}$. Despite ongoing efforts, distinguishing the many competing paired phases remains an open problem. In this work, we propose a unified theory of charge transport across a quantum point contact (QPC) for general paired FQH states described by an $so(N)_1 \times u(1)$ conformal field theory. We derive the boundary effective action for an arbitrary number of Majorana fermions $N=|\mathcal{C}_{cf}|$ and develop a non-perturbative instanton approximation to describe tunneling processes. We establish a weak-strong duality relating strong quasiparticle tunneling to weak electron tunneling. We calculate the scaling dimensions of the tunneling operators and demonstrate that while the weak-coupling fixed point is generally unstable, the strong-coupling fixed point is stable for physically relevant filling fractions and number of Majorana fermions. These transport exponents provide a distinct experimental fingerprint to identify the topological phases of even-denominator FQH states.

arXiv:2601.08792Physical review. B./Physical review. BApr 30, 20261 citation

Zero Mode Tunnelling in a Fractional Quantum Hall Device

Stephanie Jane Huntington, Vadim Cheianov

Tunnelling measurements on fractional quantum Hall systems are continuing to increase in popularity since they provide a method to probe the non-Fermi liquid behaviour of fractionally charged excitations occupying the edge states of a quantum Hall system. When considering tunnelling one must resort to an effective theory and typically a phenomenological tunnelling Hamiltonian is used analogous to that used for a conventional Luttinger liquid. It is the form of this tunnelling Hamiltonian that is investigated in this work by making a comparison to an exact microscopic calculation of the zero mode tunnelling matrix elements. The computation is performed using Monte Carlo and results were obtained for various system sizes for the $ν=1/3$ Laughlin state. Here we also present a solution to overcome the phase problem experienced in Monte Carlo calculations using Laughlin-type wavefunctions. Comparing the system size dependence of the microscopic and phenomenological calculations for the tunnelling matrix elements, it was found that only for a particular type of operator ordering in the tunnelling Hamiltonian was it possible to make a good match to the numerical calculations. From the Monte Carlo data it is also clear that for any system size the electron tunnelling is always less relevant than the quasiparticle tunnelling process, supporting the idea that when considering tunnelling at a weak barrier, the electron tunnelling process can be neglected.Tunnelling measurements on fractional quantum Hall systems are continuing to increase in popularity since they provide a method to probe the non-Fermi liquid behaviour of fractionally charged excitations occupying the edge states of a quantum Hall system. When considering tunnelling one must resort to an effective theory and typically a phenomenological tunnelling Hamiltonian is used analogous to that used for a conventional Luttinger liquid. It is the form of this tunnelling Hamiltonian that is investigated in this work by making a comparison to an exact microscopic calculation of the zero mode tunnelling matrix elements. The computation is performed using Monte Carlo and results were obtained for various system sizes for the $ν=1/3$ Laughlin state. Here we also present a solution to overcome the phase problem experienced in Monte Carlo calculations using Laughlin-type wavefunctions. Comparing the system size dependence of the microscopic and phenomenological calculations for the tunnelling matrix elements, it was found that only for a particular type of operator ordering in the tunnelling Hamiltonian was it possible to make a good match to the numerical calculations. From the Monte Carlo data it is also clear that for any system size the electron tunnelling is always less relevant than the quasiparticle tunnelling process, supporting the idea that when considering tunnelling at a weak barrier, the electron tunnelling process can be neglected.

arXiv:1410.6638Oct 24, 20143 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 $\ensuremath{\nu}=5/2$.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:0905.3607Physical Review BDec 3, 200917 citations

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.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/9503172Physical review. B, Condensed matterSep 15, 1995289 citations

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.

Even-denominator fractional quantum Hall (FQH) states can be viewed as topological superconductors of composite fermions, supporting a charged chiral mode and

|\mathcal{C}_{cf}|

neutral Majorana modes set by the Chern number

\mathcal{C}_{cf}

. Despite ongoing efforts, distinguishing the many competing paired phases remains an open problem. In this work, we propose a unified theory of charge transport across a quantum point contact (QPC) for general paired FQH states described by an

so(N)_1 \times u(1)

conformal field theory. We derive the boundary effective action for an arbitrary number of Majorana fermions

N=|\mathcal{C}_{cf}|

and develop a non-perturbative instanton approximation to describe tunneling processes. We establish a weak-strong duality relating strong quasiparticle tunneling to weak electron tunneling. We calculate the scaling dimensions of the tunneling operators and demonstrate that while the weak-coupling fixed point is generally unstable, the strong-coupling fixed point is stable for physically relevant filling fractions and number of Majorana fermions. These transport exponents provide a distinct experimental fingerprint to identify the topological phases of even-denominator FQH states.

ν=1/3

Laughlin state. Here we also present a solution to overcome the phase problem experienced in Monte Carlo calculations using Laughlin-type wavefunctions. Comparing the system size dependence of the microscopic and phenomenological calculations for the tunnelling matrix elements, it was found that only for a particular type of operator ordering in the tunnelling Hamiltonian was it possible to make a good match to the numerical calculations. From the Monte Carlo data it is also clear that for any system size the electron tunnelling is always less relevant than the quasiparticle tunnelling process, supporting the idea that when considering tunnelling at a weak barrier, the electron tunnelling process can be neglected.

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 $\ensuremath{\nu}=5/2$.

{\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.