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Fractional quantum Hall states with negative flux: edge modes in some Abelian and non-Abelian cases

Milica V. Milovanović, Th. Jolicœur

Published Jan 1, 2010• 7 citations
OpenAlex

Abstract

We investigate the structure of gapless edge modes propagating at the boundary of some fractional quantum Hall states. We show how to deduce explicit trial wavefunctions from the knowledge of the effective theory governing the edge modes. In general quantum Hall states have many edge states. Here we discuss the case of fractions having only two such modes. The case of spin-polarized and spin-singlet states at filling fraction 2/5 is considered. We give an explicit description of the decoupled charged and neutral modes. Then we discuss the situation involving negative flux acting on the composite fermions. This happens notably for the filling factor 2/3 which supports two counterpropagating modes. Microscopic wavefunctions for spin-polarized and spin-singlet states at this filling factor are given. Finally we present an analysis of the edge structure of a non-Abelian state involving also negative flux. Counterpropagating modes involve in all cases explicit derivative operators diminishing the angular momentum of the system.

Related papers

FRACTIONAL QUANTUM HALL STATES WITH NEGATIVE FLUX: EDGE MODES IN SOME ABELIAN AND NON-ABELIAN CASES

M. V. MILOVANOVIĆ, Th. Jolicœur

We investigate the structure of gapless edge modes propagating at the boundary of some fractional quantum Hall states. We show how to deduce explicit trial wavefunctions from the knowledge of the effective theory governing the edge modes. In general, quantum Hall states have many edge states. Here, we discuss the case of fractions having only two such modes. The case of spin-polarized and spin-singlet states at filling fraction ν = 2/5 is considered. We give an explicit description of the decoupled charged and neutral modes. Then we discuss the situation involving negative flux acting on the composite fermions. This happens notably for the filling factor ν = 2/3 which supports two counterpropagating modes. Microscopic wavefunctions for spin-polarized and spin-singlet states at this filling factor are given. Finally, we present an analysis of the edge structure of a non-Abelian state involving also negative flux. Counterpropagating modes involve, in all cases, explicit derivative operators diminishing the angular momentum of the system.

arXiv:0812.3764•International Journal of Modern Physics B•Feb 20, 2010•7 citations

Abelian origin of ν=2/3 and 2+2/3 fractional quantum Hall effect

Liangdong Hu, W. Zhu

We investigate the ground-state properties of the fractional quantum Hall effect at the filling factor $\ensuremath{\nu}=2/3$ and $2+2/3$, with a special focus on their typical edge physics. Via a topological characterization scheme in the framework of the density matrix renormalization group, the nature of the $\ensuremath{\nu}=2/3$ and $2+2/3$ states is identified as an Abelian hole-type Laughlin state, as evidenced by the fingerprint of entanglement spectra, central charge, and topological spin. Crucially, by constructing an interface between the $2/3$ $(2+2/3)$ state and different integer quantum Hall states, we study the structures of the interfaces from many aspects, including charge density and dipole moment. In particular, we demonstrate the edge reconstruction by visualizing edge channels comprised of two groups: the outermost $1/3$ channel and the inner composite channel made of a charged mode and neutral modes.

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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

On some quantum Hall states with negative flux

Th. Jolicœur

Some recently observed fractional quantum Hall states are not easily explained in standard hierarchy/composite fermion schemes. This paper gives a brief introduction to some wavefunctions involving non-Abelian Read-Rezayi states with negative flux that have been proposed as candidates for these new quantum Hall fractions.

arXiv:0907.1538•Jul 9, 2009•0 citations

Solvable models for neutral modes in fractional quantum Hall edges

Chris Heinrich, Michael Levin

We describe solvable models that capture how impurity scattering in certain fractional quantum Hall edges can give rise to a neutral mode---i.e., an edge mode that does not carry electric charge. These models consist of two counterpropagating chiral Luttinger liquids together with a collection of discrete impurity scatterers. Our main result is an exact solution of these models in the limit of infinitely strong impurity scattering. From this solution, we explicitly derive the existence of a neutral mode and we determine all of its microscopic properties including its velocity. We also study the stability of the neutral mode and show that it survives at finite but sufficiently strong scattering. Our results are applicable to a family of Abelian fractional quantum Hall states of which the $\ensuremath{\nu}=2/3$ state is the most prominent example.

arXiv:1702.08470•Physical review. B./Physical review. B•May 19, 2017•1 citation

Non-Abelian States with Negative Flux: A New Series of Quantum Hall States

Th. Jolicœur

By applying the idea of parafermionic clustering to composite bosons with positive as well as negative flux, a new series of trial wave functions to describe fractional quantum Hall states is proposed. These states compete at filling factors nu=k/(3k+/-2) with other ground states like stripes or composite-fermion states. These series contain all the states recently discovered by Pan et al. [Phys. Rev. Lett. 90, 016801 (2003)10.1103/Phys. Rev. Lett. 90, 016801(2003)] including the even-denominator cases. Exact diagonalization studies on the sphere and torus point to their relevance for nu=3/7, 3/11, and 3/8.

arXiv:0705.1619•Physical Review Letters•Jul 20, 2007•49 citations
We investigate the structure of gapless edge modes propagating at the boundary of some fractional quantum Hall states. We show how to deduce explicit trial wavefunctions from the knowledge of the effective theory governing the edge modes. In general quantum Hall states have many edge states. Here we discuss the case of fractions having only two such modes. The case of spin-polarized and spin-singlet states at filling fraction 2/5 is considered. We give an explicit description of the decoupled charged and neutral modes. Then we discuss the situation involving negative flux acting on the composite fermions. This happens notably for the filling factor 2/3 which supports two counterpropagating modes. Microscopic wavefunctions for spin-polarized and spin-singlet states at this filling factor are given. Finally we present an analysis of the edge structure of a non-Abelian state involving also negative flux. Counterpropagating modes involve in all cases explicit derivative operators diminishing the angular momentum of the system.
We investigate the structure of gapless edge modes propagating at the boundary of some fractional quantum Hall states. We show how to deduce explicit trial wavefunctions from the knowledge of the effective theory governing the edge modes. In general, quantum Hall states have many edge states. Here, we discuss the case of fractions having only two such modes. The case of spin-polarized and spin-singlet states at filling fraction ν = 2/5 is considered. We give an explicit description of the decoupled charged and neutral modes. Then we discuss the situation involving negative flux acting on the composite fermions. This happens notably for the filling factor ν = 2/3 which supports two counterpropagating modes. Microscopic wavefunctions for spin-polarized and spin-singlet states at this filling factor are given. Finally, we present an analysis of the edge structure of a non-Abelian state involving also negative flux. Counterpropagating modes involve, in all cases, explicit derivative operators diminishing the angular momentum of the system.
We investigate the ground-state properties of the fractional quantum Hall effect at the filling factor $\ensuremath{\nu}=2/3$ and 2+2/32+2/32+2/3, with a special focus on their typical edge physics. Via a topological characterization scheme in the framework of the density matrix renormalization group, the nature of the $\ensuremath{\nu}=2/3$ and 2+2/32+2/32+2/3 states is identified as an Abelian hole-type Laughlin state, as evidenced by the fingerprint of entanglement spectra, central charge, and topological spin. Crucially, by constructing an interface between the 2/32/32/3 (2+2/3)(2+2/3)(2+2/3) state and different integer quantum Hall states, we study the structures of the interfaces from many aspects, including charge density and dipole moment. In particular, we demonstrate the edge reconstruction by visualizing edge channels comprised of two groups: the outermost 1/31/31/3 channel and the inner composite channel made of a charged mode and neutral modes.
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 describe solvable models that capture how impurity scattering in certain fractional quantum Hall edges can give rise to a neutral mode---i.e., an edge mode that does not carry electric charge. These models consist of two counterpropagating chiral Luttinger liquids together with a collection of discrete impurity scatterers. Our main result is an exact solution of these models in the limit of infinitely strong impurity scattering. From this solution, we explicitly derive the existence of a neutral mode and we determine all of its microscopic properties including its velocity. We also study the stability of the neutral mode and show that it survives at finite but sufficiently strong scattering. Our results are applicable to a family of Abelian fractional quantum Hall states of which the $\ensuremath{\nu}=2/3$ state is the most prominent example.
By applying the idea of parafermionic clustering to composite bosons with positive as well as negative flux, a new series of trial wave functions to describe fractional quantum Hall states is proposed. These states compete at filling factors nu=k/(3k+/-2) with other ground states like stripes or composite-fermion states. These series contain all the states recently discovered by Pan et al. [Phys. Rev. Lett. 90, 016801 (2003)10.1103/Phys. Rev. Lett. 90, 016801(2003)] including the even-denominator cases. Exact diagonalization studies on the sphere and torus point to their relevance for nu=3/7, 3/11, and 3/8.