The Dirac Composite Fermion of the Fractional Quantum Hall Effect

Quantum Anomalous Hall Insulator of Composite Fermions

We show that a weak hexagonal periodic potential could transform a two-dimensional electron gas with an even-denominator magnetic filling factor to a quantum anomalous Hall insulator of composite fermions, giving rise to fractionally quantized Hall effect. The system provides a realization of the Haldane honeycomb-net model, albeit in a composite fermion system. We further propose a trial wave function for the state, and numerically evaluate its relative stability against the competing Hofstadter state. Possible sets of experimental parameters are proposed.

Coexistence of Composite-Bosons and Composite-Fermions in nu=1/2 + 1/2 Quantum Hall Bilayers

In bilayer quantum Hall systems at filling fractions near nu=1/2+1/2, as the spacing d between the layers is continuously decreased, intra-layer correlations must be replaced by inter-layer correlations, and the composite fermion (CF) Fermi seas at large d must eventually be replaced by a composite boson (CB) condensate or "111 state" at small d. We propose a scenario where CBs and CFs coexist in two interpenetrating fluids in the transition. Trial wavefunctions describing these mixed CB-CF states compare very favorably with exact diagonalization results. A Chern-Simons transport theory is con…

Composite Fermion Geometric Resonance Near ν = 1/2 Fractional Quantum Hall State

We observe geometric resonance features of composite fermions on the flanks of the even denominator ν = 1/2 fractional quantum Hall state in high-mobility two-dimensional electron and hole systems confined to wide GaAs quantum wells and subjected to a weak, strain-induced, unidirectional periodic potential modulation. The features provide a measure of how close to ν = 1/2 the system stays single-component and supports a composite fermion Fermi sea before transitioning into a ν = 1/2 fractional quantum Hall state, presumably the two-component Ψ331 state.

Hall Viscosity of the Composite-Fermion Fermi Seas for Fermions and Bosons

The Hall viscosity has been proposed as a topological property of incompressible fractional quantum Hall states and can be evaluated as Berry curvature. This paper reports on the Hall viscosities of composite-fermion Fermi seas at $ν=1/m$, where $m$ is even for fermions and odd for bosons. A well-defined value for the Hall viscosity is not obtained by viewing the $1/m$ composite-fermion Fermi seas as the $n\rightarrow \infty$ limit of the Jain $ν=n/(nm\pm 1)$ states, whose Hall viscosities $(\pm n+m)\hbar ρ/4$ ($ρ$ is the two-dimensional density) approach $\pm \infty$ in the limit $n\rightarro…

Composite fermion edge states, fractional charge and current noise

A composite fermion edge state theory of current fluctuations, fractional quasiparticle charge and Johnson-Nyquist noise in the fractional quantum Hall regime is presented. It is shown that composite fermion current fluctuations and the charges of the associated quasiparticles are strongly renormalized by the interactions between composite fermions. The important interaction is that mediated by the fictitious electric field associated with composite fermion currents. The dressed current fluctuations and quasiparticle charges are calculated self-consistently in a mean field theory for smooth ed…

Effective mass staircase and the Fermi liquid parameters for the fractional quantum Hall composite fermions

Effective mass of the composite fermion in the fractional quantum Hall system, which is of purely interaction originated, is shown, from a numerical study, to exhibit a curious nonmonotonic behavior with a staircase correlated with the number (=2,4,...) of attached flux quanta. This is surprising since the usual composite-fermion picture predicts a smooth behavior. On top of that, significant interactions are shown to exist between composite fermions, where the excitation spectrum is accurately reproduced in terms of Landau's Fermi liquid picture with negative (i.e., Hund's type) orbital and s…

Fractional charge and fractional statistics in the quantum Hall effects

Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be observed. In addition to theoretical foundations, we review the present status of the experiments in the area. We also discuss the notions of non-Abelian statistics and attempts to find experimental evidence for the existence of non-Abelian quasiparticles in certain quantum Hall systems.

Composite fermions in graphene fractional quantum Hall state at half filling: evidence for Dirac composite fermions

Composite fermions in fractional quantum Hall (FQH) systems are believed to form a Fermi sea of weakly interacting particles at half filling $ν=1/2$. Recently, it was proposed (D. T. Son, Phys. Rev. X 5, 031027 (2015)) that these composite fermions are Dirac particles. In our work, we demonstrate experimentally that composite fermions found in monolayer graphene are Dirac particles at half filling. Our experiments have addressed FQH states in high-mobility, suspended graphene Corbino disks in the vicinity of $ν=1/2$. We find strong temperature dependence of conductivity $σ$ away from half fill…

On the ground state of fractional quantum Hall effect

The paper has bene withdrawn by the author.

The Fractional Quantum Hall Effect

We give a brief introduction to the phenomenon of the Fractional Quantum Hall effect, whose discovery was awarded the Nobel prize in 1998. We also explain the composite fermion picture which describes the fractional quantum Hall effect as the integer quantum Hall effect of composite fermions.

Shot Noise and Fractional Charge at the 2/3 Composite Fractional Edge Channel

The exact structure of edge modes in `hole conjugate' fractional quantum Hall states remains an unsolved issue despite significant experimental and theoretical efforts devoted to their understanding. Recently, there has been a surge of interest in such studies led by the search for neutral modes, which in some cases may lead to exotic statistical properties of the excitations. In this letter we report on detailed measurements of shot noise, produced by partitioning of the more familiar 2/3 state. We find a fractional charge of (2/3)e at the lowest temperature, decreasing to e/3 at an elevated …

Status of the Fermi surface in mixed composite boson - composite fermion quantum Hall states

We argue that the naively expected singularities of the Fermi surface, in the mixed composite boson - composite fermion states proposed [S.H. Simon et al., PRL 91, 046803(2003)] for the evolution of ν= 1 bilayer quantum Hall system with distance, are obliterated. Our conclusion is based on a careful analysis of the momentum distribution in ν= 1/2 single-layer composite-fermion state. We point out to a possibility of the phenomenon hitherto unknown outside Kondo lattice systems when, in a translationally invariant system, Fermi-liquid-like portion of electrons enlarges its volume.

Composite Fermion Pairing in Bilayer Quantum Hall Systems

We derive the effective Hamiltonian for the composite fermion in double-layer quantum Hall systems with inter-layer tunneling at total Landau-level filling factor $ν=1/m$, where $m$ is an integer. We find that the ground state is the triplet p-wave BCS pairing state of the composite fermions. At $ν=1/2$, the ground state of the system evolves from the Halperin $(3,3,1)$-state toward the Pfaffian-state with increasing the tunneling amplitude. On the other hand, at $ν=1$, the pairing state is uniquely determined independent of tunneling amplitude.

Improved Composite-Boson Theory of Quantum Hall Ferromagnets and Skyrmions without Sigma Models

We propose an improved composite-boson theory of quantum Hall ferromagnets, where the field operator describes solely the physical degrees of freedom representing the deviation from the ground state. In this scheme skyrmions appear merely as generic excitations confined in the lowest Landau level. We evaluate the excitation energy of one skyrmion. Our theoretical estimation accounts for the activation-energy data due to Schmeller et al. remarkably well.

A Microscopic Model of Edge States of Fractional Quantum Hall Liquid: From Composite Fermions to Calogero-Sutherland Model

Based on the composite fermion approach, we derive a microscopic theory describing the low-lying edge excitations in the fractional quantum Hall liquid with $ν=\frac{ν^*}{\tildeϕν^*+1}$. For $ν^*>0$, it is found that the composite fermion model reduces to an SU$(ν^*)$ Calogero-Sutherland model in the one-dimensional limit, whereas it is not exact soluble for $ν^*<0$. However, the ground states in both cases can be found and the low-lying excitations can be shown the chiral Luttinger liquid behaviors since a gap exists between the right- and left-moving sectors in each branch of the azimuthal e…

Fractional Quantization and Fractional Quantum Hall Effect

A fractional quantization in a two dimensional space is proposed. The angular momenta of the two dimensional electrons are quantized in fractional numbers by the boundary conditions on a multi-layered Riemann surface. Extended wave functions for the incompressible quantum fluid states are presented and the cohesive and the excitation energies are given.

Pairing of Composite Fermions, Laughlin Correlations, and the Fractional Quantum Hall Hierarchy

A novel hierarchy of fractional quantum Hall (FQH) states in the lowest Landau level (LL) is proposed to explain recently observed FQH fractions such as nu=5/13, 3/8, or 4/11. Based on the analysis of their interaction pseudopotentials, it is argued that the Laughlin quasiparticles (particles/holes in a partially filled composite fermion LL) form pairs. These pairs are proposed to have Laughlin correlations with one another and to form condensed states at a sequence of fractions which includes all new fractions observed in experiment.

Topologically Protected Photonic Modes in Composite Quantum Hall/Quantum Spin Hall Waveguides

Photonic topological systems, the electromagnetic analog of the topological materials in condensed matter physics, create many opportunities to design optical devices with novel properties. We present an experimental realization of the bi-anisotropic meta waveguide photonic system replicating both quantum Hall (QH) and quantum spin-Hall (QSH) topological insulating phases. With careful design, a composite QH-QSH photonic topological material is created and experimentally shown to support reflection-free edgemodes, a heterogeneous topological structure that is unprecedented in condensed matter …

复合玻色子理论中的霍尔晶体及其向威格纳晶体的转变

Composite boson theory of Hall crystals and their transitions to Wigner crystals

本文基于复合玻色子理论研究二维电子系统在垂直磁场中的晶化过程，探讨霍尔液、威格纳晶体和霍尔晶体三种状态的转变机制，揭示霍尔晶体向威格纳晶体的连续相变特性。

Comparative Study of the Insulator-Hall Liquid-Insulator Transitions: Composite Boson Picture vs Composite Fermion Picture

Based on a newly advanced phenomenological understanding of the high-field insulator- Hall liquid transition in a composite fermion picture, we extend its composite boson counterpart to the analysis of the low-field insulator-Hall liquid transition. We thus achieve a comparative study of these two transitions. In this way, the similar reflection symmetries in filling factors in both transitions are understood consistently as due to the symmetry of the gapful excitations which dominate $σ_{xx}$ across the transitions, and the abrupt change in $σ_{xy}$ at the transitions. The substantially diffe…

Topological excitation in the Fractional Quantum Hall system

Two kinds of topological excitations, vortices and skyrmions, are studied in the frame of Ginzburg-Landau theory. We obtain the rigorous relation between the topological excitation and the order parameters in the fractional quantum Hall systems. We also discuss the evolution of the vortices in fractional quantum Hall systems.

Composite fermion model for entanglement spectrum of fractional quantum Hall states

We show that the entanglement spectrum associated with a certain class of strongly correlated many-body states --- the wave functions proposed by Laughlin and Jain to describe the fractional quantum Hall effect --- can be very well described in terms of a simple model of non-interacting (or weakly interacting) composite fermions.

Nature of quasiparticle excitations in the fractional quantum Hall effect

We investigate the 1/3 fractional quantum Hall state with one and two quasiparticle excitations. It is shown that the quasiparticle excitations are best described as excited composite fermions occupying higher composite-fermion quasi-Landau levels. In particular, the composite-fermion wave function for a single quasiparticle has 15% lower energy than the trial wave function suggested by Laughlin, and for two quasiparticles, the composite fermion theory also gives new qualitative structures.

Tunneling effect on composite fermion pairing state in bilayer quantum Hall system

We discuss the composite fermion pairing state in bilayer quantum Hall systems. After the evaluation of the range of the inter-layer separation in which the quantum Hall state is stabilized, we discuss the effect of inter-layer tunneling on the composite fermion pairing state at ν=1/2. We show that there is a cusp at the transition point between the Halperin (3,3,1) state and the Pfaffian state.

Conductance fluctuations at the fractional quantum Hall plateau transitions

We obtain a ``mean field'' scaling flow of the longitudinal and the Hall conductivities in the fractional quantum Hall regime. Using the composite fermion picture and assuming that the composite fermions follow the Khmelnitskii-Pruisken scaling flow for the integer quantum Hall effect, the unstable fixed points which govern the transitions between different fractional quantum Hall states are identified. Distributions of the critical longitudinal and Hall conductivities at the unstable fixed points are obtained and implications of the results for the experiments on mesoscopic quantum Hall syste…

Charged Excitons of Composite Fermions in the Fractional Quantum Hall Effect

Charged excitons of composite fermions (CFs) are considered in the fractional quantum Hall effect. Energies of the charged CF excitons are computed at $ν=1/3$ as a function of the size of exciton. We show that the charged CF exciton with size of roton is lower in energy than the unbound state of a neutral roton and a lone charge. Therefore we propose that the lowest-energy excitation of the fractional quantum Hall effect is in fact due to the charged excitons of composite fermions composed of two CF-particles and one CF-hole. We believe that charged excitons of composite fermions shed new ligh…

Anomalously low magnetoroton energies of the unconventional fractional quantum Hall states of composite fermions

We show a generic formation of the primary magnetorotons in the collective modes of the observed "unconventional" fractional quantum Hall effect (FQHE) states of the composite fermions at the filling factors 4/11, 4/13, 5/13, 5/17, and 3/8 at very low wavevectors with {\em anomalously} low energies which do not have any analogue to the conventional fractional quantum Hall states. Rather slow decay of the oscillations of the pair-correlation functions in these states are responsible for the low-energy magnetorotons. This is a manifestation of the distinct topology predicted before for these FQH…

Composite Fermions and the Fractional Quantum Hall Effect

The mean field (MF) composite Fermion (CF) picture successfully predicts low lying states of fractional quantum Hall systems. This success cannot be attributed to a cancellation between Coulomb and Chern-Simons interactions beyond the mean field and solely depends on the short range (SR) of the Coulomb pseudopotential in the lowest Landau level (LL). The class of pseudopotentials for which the MFCF picture can be applied is defined. The success or failure of the MFCF picture in various systems (electrons in excited LL's, Laughlin quasiparticles, charged magneto-excitons) is explained.

Fractional Quantum Hall Effect of Composite Fermions

In a GaAs/AlGaAs quantum well of electron density 1x10^{11} cm^{-2} we observe a fractional quantum Hall effect (FQHE) at filling factors nu=4/11, and 5/13, and weaker states at nu=6/17, 4/13, 5/17 and 7/11. These sequences of fractions do not fit into the standard series of integral quantum Hall effects (IQHE) of composite fermions (CF) at nu=p/(2mp +/- 1). They rather can be regarded as the FQHE of CFs attesting to residual interactions between these composite particles. In tilted magnetic fields the nu=4/11 state remains unchanged, strongly suggesting it to be spin-polarized. The weak nu=7/…

Two-Roton Bound State in the Fractional Quantum Hall Effect

The true nature of the lowest-energy, long-wavelength neutral excitation of the fractional quantum Hall effect has been a long outstanding problem. In this Letter, we establish that it is a two-roton bound state.

Magnetic Induction Dependence of Hall Resistance in Fractional Quantum Hall Effect

We constructed a Hall resistance formula for the fractional quantum Hall effect by analyzing the experimental data reported in [J. P. Eisenstein and H. L. Stormer, {Science} {\bf 248}, 1510 (1990)]. The formula is given as a function of magnetic induction, chemical potential and temperature. The Hall resistance function contains a single-electron energy spectrum, which has phenomenological perturbation terms with three tunable parameters. The formula yields 12 plateaus that are consistent with the experiment. The perturbations can be interpreted as precession or nutation of a Landau orbital in…

Topologically induced fractional Hall steps in the integer quantum Hall regime of $MoS_2$

The quantum magnetotransport properties of a monolayer of molybdenum disulfide are derived using linear response theory. Especially, the effect of topological terms on longitudinal and Hall conductivity is analyzed. The Hall conductivity exhibits fractional steps in the integer quantum Hall regime. Further complete spin and valley polarization of the longitudinal conductivity is seen in presence of these topological terms. Finally, the Shubnikov-de Hass oscillations are suppressed or enhanced contingent on the sign of these topological terms.

Improved Composite-Boson Theory of Monolayer and Bilayer Quantum Hall Ferromagnets

An improved composite-boson theory of quantum Hall ferromagnets is formulated both for the monolayer and bilayer systems. In this scheme the field operator describes solely the physical degrees of freedom representing the deviation from the ground state. Skyrmions are charged excitations confined to the lowest Landau level. By evaluating the excitation energy of one skyrmion in the interlayer-coherent phase it is shown that the bilayer QH state becomes stabler as the interlayer density difference becomes larger.

Anisotropic composite fermions and fractional quantum Hall effect

We study the role of anisotropy on the transport properties of composite fermions near Landau level filling factor $ν=1/2$ in two-dimensional holes confined to a GaAs quantum well. By applying a parallel magnetic field, we tune the composite fermion Fermi sea anisotropy and monitor the relative change of the transport scattering time at $ν=1/2$ along the principal directions. Interpreted in a simple Drude model, our results suggest that the scattering time is longer along the longitudinal direction of the composite fermion Fermi sea. Furthermore, the measured energy gap for the fractional quan…

复合玻色子与费米子的双流体理论及量子霍尔邻近效应

Two-fluid theory of composite bosons and fermions and the quantum Hall proximity effect

提出分数量子霍尔系统的双流体理论，建模其与费米液体金属界面，发现量子霍尔凝聚体渗入金属的邻近效应，并揭示带隙准电子和中性模式。

Exclusonic Quasiparticles and Thermodynamics of Fractional Quantum Hall Liquids

Quasielectrons and quasiholes in the fractional quantum Hall liquids obey fractional (including nontrivial mutual) exclusion statistics. Their statistics matrix can be determined from several possible state-counting scheme, involving different assumptions on statistical correlations. Thermal activation of quasiparticle pairs and thermodynamic properties of the fractional quantum Hall liquids near fillings $1/m$ ($m$ odd) at low temperature are studied in the approximation of generalized ideal gas. The existence of hierarchical states in the fractional quantum Hall effect is shown to be a manif…

Non-Linear hydrodynamics and Fractionally Quantized Solitons at Fractional Quantum Hall Edge

We argue that dynamics of gapless Fractional Quantum Hall Edge states is essentially non-linear and that it features fractionally quantized solitons propagating along the edge. Observation of solitons would be a direct evidence of fractional charges. We show that the non-linear dynamics of the Laughlin's FQH state is governed by the quantum Benjamin-Ono equation. Non-linear dynamics of gapless edge states is determined by gapped modes in the bulk of FQH liquid. The dispersion of edge modes is traced to the double boundary layer of FQH states.

Paired composite fermion phase of quantum Hall bilayers at ν= 1/2 + 1/2

We provide numerical evidence for composite fermion pairing in quantum Hall bilayer systems at filling $ν=1/2 + 1/2$ for intermediate spacing between the layers. We identify the phase as $p_x + i p_y$ pairing, and construct high accuracy trial wavefunctions to describe the groundstate on the sphere. For large distances between the layers, and for finite systems, a competing "Hund's rule" state, or composite fermion liquid, prevails for certain system sizes. We argue that for larger systems, the pairing phase will persist to larger layer spacing.

High field fractional quantum Hall effect in optical lattices

We consider interacting bosonic atoms in an optical lattice subject to a large simulated magnetic field. We develop a model similar to a bilayer fractional quantum Hall system valid near simple rational numbers of magnetic flux quanta per lattice cell. Then we calculate its ground state, magnetic lengths, fractional fillings, and find unexpected sign changes in the Hall current. Finally we study methods for detecting these novel features via shot noise and Hall current measurements.

Activation energies for spin-reversed excitations in the fractional quantum Hall effect

The activation energy measured in transport experiments in the fractional Hall regime corresponds to the energy required to create a far separated particle hole pair. We calculate, for several fractional quantum Hall states, the energy gaps for the excitation in which the excited composite fermion reverses its spin quantum number. Our results indicate that such spin reversed excitations may be relevant in experimentally accessible regimes.

Paired fractional quantum Hall states and the nu=5/2 puzzle

Work on the problem of the $ν=5/2$ fractional quantum Hall state is reviewed, with emphasis on recent progress concerning paired states.

Fractional quantum Hall effect without energy gap

In the fractional quantum Hall effect regime we measure diagonal ($ρ_{xx}$) and Hall ($ρ_{xy}$) magnetoresistivity tensor components of two-dimensional electron system (2DES) in gated GaAs/Al$_{x}$Ga$_{1-x}$As heterojunctions, together with capacitance between 2DES and the gate. We observe 1/3- and 2/3-fractional quantum Hall effect at rather low magnetic fields where corresponding fractional minima in the thermodynamical density of states have already disappeared manifesting complete suppression of the quasiparticle energy gaps.

Statistics of composite fermions in the quantum hall effect

The High Landau level filling fractions 5/2, 7/3 and 8/3 are interpreted by using the angular momentum model. It is found that for the odd number of flux quanta, the quasiparticles called the ``composite fermions'' are fermions but for even number-, the quasiparticles are a mixture of bosons and fermions. Therefore, the theory of ``composite fermions'' is internally inconsistent.

The stability of the fractional quantum Hall effect in topological insulators

With the recent observation of graphene-like Landau levels at the surface of topological insulators, the possibility of fractional quantum Hall effect, which is a fundamental signature of strong correlations, has become of interest. Some experiments have reported intra-Landau level structure that is suggestive of fractional quantum Hall effect. This paper discusses the feasibility of fractional quantum Hall effect from a theoretical perspective, and argues that while this effect should occur, ideally, in the $n=0$ and $|n|=1$ Landau levels, it is ruled out in higher $|n|$ Landau levels. Unlike…

Experimental Test of Condensate-Excitation Theories of the Fractional Quantum Hall Effect

It is shown that the description of the FQHE as condensation of the electron system into a ground state with fractionally charged excitations is incompatible with experimental observations. The nature of the Hall voltage in fractional plateaux as a chemical potential difference eliminates the condensate as current carrier and the temperature dependence of longitudinal conductance eliminates the excitation picture of charge carriers.

Edge reconstructions in fractional quantum Hall systems

Two dimensional electron systems exhibiting the fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges where gapless excitations are present. We present a {\it microscopic} calculation of the edge states in the fractional quantum Hall systems at various filling factors using the extended Hamiltonian theory of the fractional quantum Hall effect. We find that at $ν=1/3$ the quantum Hall edge undergoes a reconstruction as the background potential softens, whereas quantum Hall edges at hi…

Composite Fermions Phenomenology in Quantum Hall Effect

An effort is made to understand the phenomenological composite fermion model of the quantum Hall effect. The odd denominators are composed by adding plus minus 1 to the even numbers 2, 4, 6 and 8. Although the denominators are phenomenologically made to agree with the experimental data, the physics of the CF model, i.e., the even flux quanta attachment to the electron is found to be incorrect.

Fractional Quantum Hall Hierarchy and the Second Landau Level

We generalize the fractional quantum Hall hierarchy picture to apply to arbitrary, possibly non-Abelian, fractional quantum Hall states. Applying this to the nu = 5/2 Moore-Read state, we construct new explicit trial wavefunctions to describe the fractional quantum Hall effect in the second Landau level. The resulting hierarchy of states, which reproduces the filling fractions of all observed Hall conductance plateaus in the second Landau level, is characterized by electron pairing in the ground state and an excitation spectrum that includes non-Abelian anyons of the Ising type. We propose thi…

Dependence of the Fractional Quantum Hall Edge Critical Exponent on the Range of Interaction

Comment on A.M.Chang et al, PRL 86, 143 (2001).

Composite fermions in the Fractional Quantum Hall Effect: Transport at finite wavevector

We consider the conductivity tensor for composite fermions in a close to half-filled Landau band in the temperature regime where the scattering off the potential and the trapped gauge field of random impurities dominates. The Boltzmann equation approach is employed to calculate the quasiclassical transport properties at finite effective magnetic field, wavevector and frequency. We present an exact solution of the kinetic equation for all parameter regimes. Our results allow a consistent description of recently observed surface acoustic wave resonances and other findings.

Quantum Hall effect at half-filled Landau level: Pairing of composite fermions

We discuss the possibility of the quantum Hall effect at half-filled Landau level in terms of the pairing of the composite fermions. In the absence of Coulomb energy, we show that the ground state of the system is described by the {\it p}-wave BCS pairing state of composite fermions. When the ratio $α\equiv (e^2/ε\ell_B)/ε_F$ ($\ell_B$ : the magnetic length, $ε_F$ : Fermi energy of the composite fermions) is larger than a critical value $α_c \sim 8.2$ the gap of the pairing state vanishes. However, $α$ remains less than $α_c$ if $\hbar ω_c \gg e^2/ε\ell_B$ holds. Then in this situation it is p…

Abelian and Non-abelian Hall Liquids and Charge Density Wave: Quantum Number Fractionalization in One and Two Dimensions

Previously we have demonstrated that, on a torus, the abelian quantum hall liquid is adiabatically connected to a charge density wave as the smaller dimension of the torus is varied. In this work we extend this result to the non-abelian bosonic Hall state. The outcome of these works is the realization that the paradigms of quantum number fractionalization in one dimension (polyacetylene) and two dimensions (fractional quantum Hall effect) are in fact equivalent.

Shot-noise evidence of fractional quasiparticle creation in a local fractional quantum Hall state

We have experimentally identified fractional quasiparticle creation in a tunneling process through a local fractional quantum Hall (FQH) state. The local FQH state is prepared in a low-density region near a quantum point contact (QPC) in an integer quantum Hall (IQH) system. Shot-noise measurements reveal a clear transition from elementary-charge tunneling at low bias to fractional-charge tunneling at high bias. The fractional shot noise is proportional to T1(1 ? T1) over a wide range of T1, where T1 is the transmission probability of the IQH edge channel. This binomial distribution indicates …

Microscopic origin of the next generation fractional quantum Hall effect

Most of the fractions observed to date belong to the sequences $ν=n/(2pn\pm 1)$ and $ν=1-n/(2pn\pm 1)$, $n$ and $p$ integers, understood as the familiar {\em integral} quantum Hall effect of composite fermions. These sequences fail to accommodate, however, many fractions such as $ν=4/11$ and 5/13, discovered recently in ultra-high mobility samples at very low temperatures. We show that these "next generation" fractional quantum Hall states are accurately described as the {\em fractional} quantum Hall effect of composite fermions.