It was recently discovered that fractional quantum Hall (FQH) states can be classified by the way ground state wave functions go to zero when electrons are brought close together. Quasiparticles in the FQH states can be classified in a similar way, by the pattern of zeros that result when electrons are brought close to the quasiparticles. In this paper we combine the pattern-of-zero approach and the conformal-field-theory (CFT) approach to calculate the topological properties of quasiparticles. We discuss how the quasiparticles in FQH states naturally form representations of a magnetic translation algebra, with members of a representation differing from each other by Abelian quasiparticles. We find that this structure dramatically simplifies topological properties of the quasiparticles, such as their fusion rules, charges, and scaling dimensions, and has consequences for the ground state degeneracy of FQH states on higher genus surfaces. We find constraints on the pattern of zeros of quasiparticles that can fuse together, which allow us to obtain the fusion rules of quasiparticles from their pattern of zeros, at least in the case of the (generalized and composite) parafermion states. We also calculate from CFT the number of quasiparticle types in the generalized and composite parafermion states, which confirm the result obtained previously through a completely different approach.
We report localization of fractional quantum Hall (QH) quasiparticles on graphene antidots. By studying coherent tunneling through the localized QH edge modes on the antidot, we measured the QH quasiparticle charges to be approximately $\pm e/3$ at fractional fillings of $ν= \pm 1/3$. The Dirac spectrum in graphene allows large energy scales and robust quasiparticle localization against thermal excitation. The capability of localizing fractional quasiparticles on QH antidots brings promising opportunities for realizing anyon braiding and novel quantum electronics.
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 …
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.
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…
Quasiparticles of the fractional quantum Hall systems obey fractional (including mutual) exclusion statistics. In this note we study the effects of exclusion statistics on thermal activation of quasiparticle pairs in the approximation of generalized ideal gas. The distribution function for thermally activated quasiparticles is found explicitly for the statistics matrix given by the composite fermion picture and the thermodynamic consequences are discussed analytically. In particular, at low temperatures, there is a quasielectron-quasihole duality in the description of the system between two ad…
Shot noise measurements were recently exploited to measure the charge of the quasiparticles in the Fractional Quantum Hall (FQH) regime. For fractional filling factors nu=1/3 and 2/5 of the first Landau level, fractional charges q=e/3 and e/5, respectively, were measured. We investigate here the interaction of e/3 quasiparticles with a strong backscatterer and find unexpected results. When a weak backscatterer is introduced in the path of an otherwise noiseless current of quasiparticles, stochastic partitioning of the quasiparticles takes place and shot noise proportional to their charge appea…
It is well-known that Lorentzian voltage pulses with integer quantum flux can lead to noiseless current in quantum conductors. The current is carried by charged quasiparticles in the Fermi sea of the conductors, which have well-defined wave functions and have been named as "levitons". However, it is not clear how levitons evolve as the flux of the pulses changes continuously toward a fractional value. To answer this question, we introduce a set of Wannier-like single-body wave functions, which can be used to describe the quantum states of the quasiparticles injected by Lorentzian pulses with a…
Starting from a collective description of the incompressible fractional quantum Hall liquid as an elastic medium that supports gapped neutral excitations I show that the one-electron spectral function of this system exhibits a sharp peak at the lowest available excitation energy, well separated from the continuum spectrum at higher energy. I interpret this peak as the signature of the integral charge quasiparticle recently predicted by Peterson and Jain\cite{Jain05}, and calculate its spectral weight for different filling factors.
Remarkable nonlinearities in the differential tunneling conductance between fractional quantum Hall edge states at a constriction are observed in the weak-backscattering regime. In the $ν$ = 1/3 state a peak develops as temperature is increased and its width is determined by the fractional charge. In the range $2/3 \le ν\le 1/3$ this width displays a symmetric behavior around $ν$ = 1/2. We discuss the consistency of these results with available theoretical predictions for inter-edge quasiparticle tunneling in the weak-backscattering regime.
We have considered here the statistics parameter for quasiparticles in FQH states from an analysis of these states in the framework of chiral anomaly and Berry phase. It is shown that we have a generalized relation such that the statistical phase of a quasiparticle for FQH states at $ν=p/q$ with $p(q)$ even or odd, is given by $e^{iπθ}$ with $θ=p/q $ and the charge is $-e \frac{p}{q}$. The statistics parameter for a quasihole is identical with that of a quasiparticle and the charge is of opposite sign.
The pseudopotentials describing the interactions of quasiparticles in fractional quantum Hall (FQH) states are studied. Rules for the identification of incompressible quantum fluid ground states are found, based upon the form of the pseudopotentials. States belonging to the Jain sequence nu=n/(1+2pn), where n and p are integers, appear to be the only incompressible states in the thermodynamic limit, although other FQH hierarchy states occur for finite size systems. This explains the success of the composite Fermion picture.
We make a semiclassical analysis of thermal pair creations of quasiparticles at various filling factors in quantum Hall systems. It is argued that the gap energy is reduced considerably by the Coulomb potential made by impurities. It is also shown that a tunneling process becomes important at low temperature and at strong magnetic field. We fit typical experimental data excellently based on our semiclassical results of the gap energy.
We present a microscopic theory of ground-state spectral function of bilayer quantum Hall systems that includes interactions between Hartree-Fock quasiparticles and quantum fluctuations of the order parameter field. The collective modes in these systems are properly described only when fluctuations in direct and exchange particle-hole channels are taken into account. Using an auxiliary field functional integral approach, we present a generalization of the random phase approximation \emph{for quasiparticle self-energy} which captures fluctuations in both channels. We discuss its relationship to…
Quasiparticle spin (in the spacetime sense) couples to curvature of space. Here this fact is used to calculate the spin of quasiholes in trial quantum Hall states by adiabatically dragging them around on a sphere, for trial states given by conformal blocks in some conformal field theory. The spin is found to agree with the conformal weight of the corresponding field. The result completes a recent argument that constructions using blocks from non-unitary theories that contain negative quantum dimensions produce contradictions that prevent them from describing topological (gapped) phases of matt…
Theory predicts that quasiparticle tunneling between the counter-propagating edges in a fractional quantum Hall state can be used to measure the effective quasiparticle charge e* and dimensionless interaction parameter g, and thereby characterize the many-body wavefunction describing the state. We report measurements of quasiparticle tunneling in a high mobility GaAs two dimensional electron system in the fractional quantum Hall state at nu=5/2 using a gate-defined constriction to bring the edges close together. We find the dc-bias peaks in the tunneling conductance at different temperatures c…
The energy, interaction, and optical properties of reversed-spin quasielectrons (QE_R's) in fractional quantum Hall systems are studied. Based on the short range of the QE_R-QE_R repulsion, a partially unpolarized incompressible nu=4/11 state is postulated within Haldane hierarchy scheme. To describe photoluminescence, a reversed-spin fractionally charged exciton hQE_R (QE_R bound to a valence hole h) is predicted. In contrast to its spin-polarized analog, hQE_R is strongly bound and radiative.
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…
Laboratory of Atomic and Solid State Physics, Cornell University（康奈尔大学原子与固态物理实验室）；School of Applied and Engineering Physics, Cornell University（康奈尔大学应用工程物理学院）；Research Center for Functional Materials, National Institute for Materials Science（日本国立材料研究所功能材料研究中心）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（日本国立材料研究所电子光学材料研究中心）
Electron correlation in a quantum many-body state appears as peculiar scattering behaviour at its boundary, symbolic of which is Andreev reflection at a metal-superconductor interface. Despite being fundamental in nature, dictated by the charge conservation law, however, the process has had no analogues outside the realm of superconductivity so far. Here, we report the observation of an Andreev-like process originating from a topological quantum many-body effect instead of superconductivity. A narrow junction between fractional and integer quantum Hall states shows a two-terminal conductance e…
From the analysis of their interaction pseudopotentials, it is argued that (at certain filling factors) Laughlin quasiparticles can form pairs. It is further proposed that such pairs could have Laughlin correlations with one another and form condensed states of a new type. The sequence of fractions corresponding to these states includes all new fractions observed recently in experiment (e.g., ν=5/13, 3/8, or 4/11).
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 charge e/4 (non-Abelian) and e/2 (Abelian) may co-exist 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…
Low lying excitations of electron liquids in the fractional quantum Hall (FQH) regime are studied by resonant inelastic light scattering methods. We present here results from charge and spin excitations of FQH states in the lowest spin-split Landau levels that are of current interest. In the range of filling factors $2/5 \geq ν\geq 1/3$, we find evidence that low energy quasiparticle excitations can be interpreted with spin-split composite fermion quasi-Landau levels. At FQH states around $ν=3/2$, we find well-defined excitations at 4/3 and 8/5 that are consistent with a spin-unpolarized popul…
It has been pointed out by Smet that there are fractional-charge values which do not fit with their formula of composite fermions. We find that our formula predicts these fractional charges very well and in fact there exists a relationship between spin and charge of a quasiparticle.
We study the magneto-conductance of a $1.4~\mathrm{μm}$-wide quantum dot in the fractional quantum Hall regime. For a filling factor $\approx 2/3$ and $\gtrsim 1/3$ in the quantum dot the observed Coulomb resonances show a periodic modulation in magnetic field. This indicates a non-trivial reconstruction of the 2/3 fractional quantum Hall state in the quantum dot. We present a model for the charge stability diagram of the system assuming two compressible regions separated by an incompressible stripe of filling factor $2/3$ and $1/3$, respectively. From the dependence of the magnetic field peri…
We have studied here the charge and statistics of quasiparticle excitations in FQH states on the basis of the Berry phase approach incorporating the fact that even number of flux quanta can be gauged away when the Berry phase is removed to the dynamical phase. It is observed that the charge $q$ and statistical parameter $θ$ of a quasiparticle at filling factor $ν=\frac{n}{2pn+1}$ are given by $q=(\frac{n}{2pn+1})e$ and $θ=\frac{n}{2pn+1}$, with the fact that the charge of the quasihole is opposite to that of the quasielectron. Using Laughlin wave function for quasiparticles, numerical studies …
New low-lying excitations are observed by inelastic light scattering at filling factors $ν=p/(ϕp \pm 1)$ of the fractional quantum Hall regime with $ϕ=4$. Coexisting with these modes throughout the range $ν\leq 1/3$ are $ϕ=2$ excitations seen at 1/3. Both $ϕ=2$ and $ϕ=4$ excitations have distinct behaviors with temperature and filling factor. The abrupt first appearance of the new modes in the low energy excitation spectrum at $ν\lesssim 1/3$ suggests a marked change in the quantum ground state on crossing the $ϕ=2 \to ϕ=4$ boundary at $ν= 1/3$.
We consider the quantum Hall effect induced by magnetic field and rotation, which can drive the Hall samples into the quantum Hall regime and induce fractional excitations. Both the mass and the charge of the Laughlin quasiparticles are predicted to be fractionally quantized. The observable effects induced by rotation are discussed. Based on the usual Hall samples under rotation, we propose an experimental setup for detecting the macroscopic quantization phenomena and the fractional mass of the Laughlin quasiparticles.
Using the Onsager relation between electric and heat transport coefficients, and considering the very different roles played by the quantum Hall condensate and quasiparticles in transport, we argue that near the center of a quantum Hall plateau thermopower in a Corbino geometry measures {\it "entropy per quasiparticle per quasiparticle charge"}. This relation indicates that thermopower measurement in a Corbino setup is a more direct measure of quasiparticle entropy than in a Hall bar. Treating disorder within the self-consistent Born approximation, we show through an explicit microscopic calcu…
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.
We propose an approach that enables implementation of anyonic quantum computation in systems of antidots in the two-dimensional electron liquid in the FQHE regime. The approach is based on the adiabatic transfer of FQHE quasiparticles in the antidot systems, and uses their fractional statistics to perform quantum logic. Advantages of our scheme over other semiconductor-based proposals of quantum computation include the energy gap in the FQHE liquid that suppresses decoherence, and the topological nature of quasiparticle statistics that makes it possible to entangle two quasiparticles without t…
We report experiments on electron interferometer devices in the quantum Hall regime, where edge channels circle a 2D electron island. The main confinement is produced by etch trenches, into which front gate metal is deposited. We find a linear dependence of the Aharonov-Bohm period on gate voltage for electrons (integer filling f=1) and for Laughlin quasiparticles (fractional 2/5 embedded in 1/3). The capacitance of a large 2D electron island with respect to the front gates is approximately proportional to the island radius. Comparing the experimental data for the integer and the fractional fi…
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.
We present a theory of the photovoltaic valley-dependent Hall effect in a two-dimensional Dirac semiconductor subject to an intense near-resonant electromagnetic field. Our theory captures and elucidates the influence of both the field-induced resonant interband transitions and the nonequilibrium carrier kinetics on the resulting valley Hall transport in terms of photon-dressed quasiparticles. The non-perturbative renormalization effect of the pump field manifests itself in the dynamics of the photon-dressed quasiparticles, with a quasienergy spectrum characterized by {dynamical gaps $δ_η$ ($η…
Microwave response of fractional quantum Hall droplets with quasiparticle tunneling
Institute for Solid State Physics, University of Tokyo（东京大学固体物理研究所）；Aix Marseille Univ, Université de Toulon, CNRS, CPT（艾克斯-马赛大学，土伦大学，法国国家科学研究中心，理论物理中心）
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.
We study transport through an electronic Mach-Zehnder interferometer recently devised at the Weizmann Institute. We show that this device can be used to probe statistics of quasiparticles in the fractional quantum Hall regime. We calculate the tunneling current through the interferometer as the function of the Aharonov-Bohm flux, temperature and voltage bias, and demonstrate that its flux-dependent component is strongly sensitive to the statistics of tunneling quasiparticles. More specifically, the flux-dependent and flux-independent contributions to the current are related by a power law, the…
The low energy physics of the fractional Hall liquid is described in terms quasiparticles that are qualitatively distinct from electrons. We show, however, that a long-lived electron-like quasiparticle also exists in the excitation spectrum: the state obtained by the application of an electron creation operator to a fractional quantum Hall ground state has a non-zero overlap with a complex, high energy bound state containing an odd number of composite-fermion quasiparticles. The electron annihilation operator similarly couples to a bound complex of composite-fermion holes. We predict that thes…
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.
Strongly correlated low-dimensional systems can host exotic elementary excitations carrying a fractional charge $q$ and potentially obeying anyonic statistics. In the fractional quantum Hall effect, their fractional charge has been successfully determined owing to low frequency shot noise measurements. However, a universal method for sensing them unambiguously and unraveling their intricate dynamics was still lacking. Here, we demonstrate that this can be achieved by measuring the microwave photons emitted by such excitations when they are transferred through a potential barrier biased with a …
A device is proposed that is similar in spirit to the electron turnstile except that it operates within a quantum Hall fluid. In the integer quantum Hall regime, this device pumps an integer number of electrons per cycle. In the fractional regime, it pumps an integer number of fractionally charged quasiparticles per cycle. It is proposed that such a device can make an accurate measurement of the charge of the quantum Hall effect quasiparticles.
A microscopic confirmation of the fractional statistics of the {\em quasiparticles} in the fractional quantum Hall effect has so far been lacking. We calculate the statistics of the composite-fermion quasiparticles at $ν=1/3$ and $ν=2/5$ by evaluating the Berry phase for a closed loop encircling another composite-fermion quasiparticle. A careful consideration of subtle perturbations in the trajectory due to the presence of an additional quasiparticle is crucial for obtaining the correct value of the statistics. The conditions for the applicability of the fractional statistics concept are discu…
We show in this paper that thermopower is enhanced in non-Abelian quantum Hall liquids under appropriate conditions. This is because thermopower measures entropy per electron in the clean limit, while the degeneracy and entropy associated with non-Abelian quasiparticles enhance entropy when they are present. Thus thermopower can potentially probe non-Abelian nature of the quasiparticles, and measure their quantum dimension.
We study a delocalization transition for non-interacting quasiparticles moving in two dimensions, which belongs to a new symmetry class. This symmetry class can be realised in a dirty, gapless superconductor in which time reversal symmetry for orbital motion is broken, but spin rotation symmetry is intact. We find a direct transition between two insulating phases with quantized Hall conductances of zero and two for the conserved quasiparticles. The energy of quasiparticles acts as a relevant, symmetry-breaking field at the critical point, which splits the direct transition into two conventiona…
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…
Recent schemes for experimentally probing non-abelian statistics in the quantum Hall effect are based on geometries where current-carrying quasiparticles flow along edges that encircle bulk quasiparticles, which are localized. Here we consider one such scheme, the Fabry-Perot interferometer, and analyze how its interference patterns are affected by a coupling that allows tunneling of neutral Majorana fermions between the bulk and edge. While at weak coupling this tunneling degrades the interference signal, we find that at strong coupling, the bulk quasiparticle becomes essentially absorbed by …
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.
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…
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.
We discuss how one-dimensional interacting fermion systems, which in the low energy approximation are described by Luttinger liquid theory, can be reformulated as systems of weakly interacting particles with fractional charge and statistics. Our approach is to use Landau's phenomenological approach to Fermi liquid theory, where the quasiparticles are interpreted as adiabatically dressed fermions. In an earlier publication the local charge carried by these excitations has been shown to be fractional. We focus here on the statistics of the quasiparticles and show that by a change of momentum var…
In the experiments, the quantity measurd is the product of the charge and the magnetic field from which fractional charge is deduced. There is no objection to measuring the fractional charge as long as it is remembered that the product of the charge and the field has been measured. So If the fraction came from the field rather than from the charge, the experiment will remain unaffected. There is no prescription about the mass splitting so there is no way to combine two masses into one. Therefore, the fractional charge can be obtained by changing the state of the quasiparticle without splitting…
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.
Determination of properties of quasiparticle excitations is an important task in the experimental investigation of the fractional quantum Hall effect (FQHE). We propose a model-independent method for finding the scaling dimension of FQHE quasiparticles from measurements of the electric current tunneling between two FQHE edges and its noise. In comparison to the commonly used method based on measuring the tunneling current only, the proposed method is less prone to the errors due to non-universal physics of tunnel junctions.
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.
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.
