Fractional Quantum Hall Plateau Research Articles

3/2 fractional quantum Hall plateau in confined two-dimensional electron gas

Even-denominator fractional quantum Hall (FQH) states, such as 5/2 and 7/2, have been well known in a two-dimensional electron gas (2DEG) for decades and are still investigated as candidates of non-Abelian statistics. In this paper, we present the observation of a 3/2 FQH plateau in a single-layer 2DEG with lateral confinement at a bulk filling factor of 5/3. The 3/2 FQH plateau is quantized at left( {frac{h}{{e^2}}} right)/left( {frac{3}{2}} right) within 0.02%, and can survive up to 300 mK. This even-denominator FQH plateau may imply intriguing edge structure and excitation in FQH system with lateral confinement. The observations in this work demonstrate that understanding the effect of the lateral confinement on the many-body system is critical in the pursuit of important theoretical proposals involving edge physics, such as the demonstration of non-Abelian statistics and the realization of braiding for fault-tolerant quantum computation.

Fractional quantum Hall effects in In0.75Ga0.25As bilayer electron systems observed as \u201cFinger print\u201d

Observations of fractional quantum Hall (FQH) plateaus are reported in bilayer electron gas system in wide (>80 nm) In0.75Ga0.25As wells. Several q/p (p = 5, 3, and 2, q > 5) QH states are confirmed at high temperatures (~1.6 K) when the critical conditions including an electron density imbalance as well as a dynamical resistance behavior at the bilayer-monolayer transition are properly satisfied. The former leads to a quantum limit in either of the layers and the latter might bring a meta-stable nature into FQH phenomena. Such a behavior occurs as a probability process associating with impurities or defects in the wells, they inevitably reflect the local structural landscapes of each sample. This is verified by the new finding that the kinds of fractional plateaus (what set of fractional filling factors) appeared are different depending on the samples, that is, they are the “finger print” in each sample.

Fractional Quantum Conductance Plateaus in Mosaic‐Like Conductors and Their Similarities to the Fractional Quantum Hall Effect

AbstractA simple route to generate magnetotransport data is reported that results in fractional quantum Hall plateaus in the conductance without invoking strongly correlated physics. Ingredients to the generating model are conducting tiles with integer quantum Hall effect and metallic linkers, further Kirchhoff rules. When connecting few identical tiles in a mosaic, fractional steps occur in the conductance values. Richer spectra representing several fractions occur when the tiles are parametrically varied. Parts of the simulation data are supported with purposefully designed graphene mosaics in high magnetic fields. The findings emphasize that the occurrence of fractional conductance values, in particular in two‐terminal measurements, does not necessarily indicate interaction‐driven physics. The importance of an independent determination of charge densities is underscored and similarities with and differences to the fractional quantum Hall effect are critically discussed.

Non-Abelian fermionization and fractional quantum Hall transitions

There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the half-filled Landau level. Here, we study the application of one such duality to the long-standing problem of quantum Hall inter-plateaux transitions. The key motivating experimental observations are the anomalously large value of the correlation length exponent $\nu \approx 2.3$ and that $\nu$ is observed to be super-universal, i.e., the same in the vicinity of distinct critical points. Duality motivates effective descriptions for a fractional quantum Hall plateau transition involving a Chern-Simons field with $U(N_c)$ gauge group coupled to $N_f = 1$ fermion. We study one class of theories in a controlled limit where $N_f \gg N_c$ and calculate $\nu$ to leading non-trivial order in the absence of disorder. Although these theories do not yield an anomalously large exponent $\nu$ within the large $N_f \gg N_c$ expansion, they do offer a new parameter space of theories that is apparently different from prior works involving abelian Chern-Simons gauge fields.

Fibonacci anyons and charge density order in the 12/5 and 13/5 quantum Hall plateaus

The $\nu=12/5$ fractional quantum Hall plateau observed in $\mathrm{GaAs}$ semiconductor wells is a suspect in the search for non-Abelian Fibonacci anyons. Using the infinite density matrix renormalization group, we find clear evidence that fillings $\nu = 12/5$ and $\nu=13/5$ are in the $k = 3$ Read-Rezayi phase in the absence of particle-hole symmetry-breaking effects. The lowest energy charged excitation is identified as a non-Abelian Fibonacci anyon, distinguished from its Abelian counterpart by its local quadrupole moment. However, several experiments at $\nu = 13/5$ observe a re-entrant integer quantum Hall effect, implying particle-hole symmetry is broken. We rule out spin polarization as the origin of the asymmetry. Further, we point out extremely close energetic competition between the Read-Rezayi phase and a re-entrant integer quantum Hall phase. This competition suggests that even small particle-hole symmetry-breaking perturbations can explain the experimentally observed asymmetry between $\nu = 12/5$ and $13/5$. We find that at $\nu=12/5$ Landau level mixing favors the Read-Rezayi phase over the re-entrant phase.

Topological Blockade and Measurement of Topological Charge

The fractionally charged quasiparticles appearing in the 5/2 fractional quantum Hall plateau are predicted to have an extra nonlocal degree of freedom, known as topological charge. We show how this topological charge can block the tunneling of these particles, and how such topological blockade can be used to read out their topological charge. We argue that the short time scale required for this measurement is favorable for the detection of the non-Abelian anyonic statistics of the quasiparticles. We also show how topological blockade can be used to measure braiding statistics, and to couple a topological qubit with a conventional one.

Quasiparticles and excitons for the Pfaffian quantum Hall state

We propose trial wave functions for quasiparticle and exciton excitations of the Moore-Read Pfaffian fractional quantum Hall states, both for bosons and for fermions, and study these numerically. Our construction of trial wave functions employs a picture of the bosonic Moore-Read state as a symmetrized double layer composite fermion state. We obtain the number of independent angular momentum multiplets of quasiparticle and exciton trial states for systems of up to 20 electrons. We find that the counting for quasielectrons at large angular momentum on the sphere matches that expected from the conformal field theory (CFT) that describes the Moore-Read state's boundary theory. In particular, the counting for quasielectrons is the same as for quasiholes, in accordance with the idea that the CFT describing both sides of the Fractional Quantum Hall plateau should be the same. We also show that our trial wave functions have good overlaps with exact wave functions obtained using various interactions, including second Landau level Coulomb interactions and the three-body delta interaction for which the Pfaffian states and their quasiholes are exact ground states. We discuss how these results relate to recent work by Sreejith et al. on a similar set of trial wave functions for excitations over the Pfaffian state as well as to earlier work by Hansson et al., which has produced trial wave functions for quasiparticles based on conformal field theory methods and by Bernevig and Haldane, which produced trial wave functions based on clustering properties and ``squeezing.''

A direct connection between quantum Hall plateaus and exact pair states in a 2D electron gas

AbstractIt is previously found that the two-dimensional (2D) electron-pair in a homogeneous magnetic field has a set of exact solutions for a denumerably infinite set of magnetic fields. Here we demonstrate that as a function of magnetic field a band-like structure of energy associated with the exact pair states exists. A direct and simple connection between the pair states and the quantum Hall effect is revealed by the band-like structure of the hydrogen “pseudo-atom”. From such a connection one can predict the sites and widths of the integral and fractional quantum Hall plateaus for an electron gas in a GaAs-AlxGa1−x As heterojunction. The results are in good agreement with the existing experimental data.

Interferometric signature of non-Abelian anyons

We consider the tunneling current through a double point-contact Fabry-P\'erot interferometer such as used in recent experimental studies of the fractional quantum Hall plateau at filling fraction $\ensuremath{\nu}=5/2$. We compare the predictions of several different models of the state of the electrons at this plateau: the Moore-Read, anti-Pfaffian, $\text{SU}{(2)}_{2}$ NAF, $K=8$ strong pairing, and (3,3,1) states. All of these predict the existence of charge $e/4$ quasiparticles, but the first three are non-Abelian while the last two are Abelian. We give explicit formulas for the scaling of charge $e/2$ and charge $e/4$ quasiparticle contributions to the current as a function of temperature, gate voltage, and distance between the two point contacts for all three models. Based on these, we analyze several possible explanations of two phenomena reported for recent experiments by Willett et al., namely, halving of the period of the observed resistance oscillations with rising temperature and alternation between the same two observed periods at low temperatures as the area of the interference loop is varied with a side gate. We conclude that the most likely explanation is that the observed alternation is due to switching between even and odd numbers of charge $e/4$ quasiparticles enclosed within the loop as a function of side-gate voltage, which is a clear signature of the presence of non-Abelian anyons. However, there are important features of the data which do not have a simple explanation within this picture. We suggest further experiments which could help rule out some possible scenarios. We make the corresponding predictions for future tunneling and interference experiments at the other observed second Landau level fractional quantum Hall states.

ABJM with flavors and FQHE

We add fundamental matters to the N=6 Chern-Simons theory (ABJM theory), and show that D6-branes wrapped over AdS_4 x S^3/Z_2 in type IIA superstring theory on AdS_4 x CP^3 give its dual description with N=3 supersymmetry. We confirm this by the arguments based on R-symmetry, supersymmetry, and brane configuration of ABJM theory. We also analyze the fluctuations of the D6-brane and compute the conformal dimensions of dual operators. In the presence of fractional branes, the ABJM theory can model the fractional quantum Hall effect (FQHE), with RR-fields regarded as the external electric-magnetic field. We show that an addition of the flavor D6-brane describes a class of fractional quantum Hall plateau transition.

Interactions suppress quasiparticle tunneling at Hall bar constrictions.

Tunneling of fractionally charged quasiparticles across a two-dimensional electron system on a fractional quantum Hall plateau is expected to be strongly enhanced at low temperatures. This theoretical prediction is at odds with recent experimental studies of samples with weakly pinched quantum-point-contact constrictions in which the opposite behavior is observed. We argue here that this unexpected finding is a consequence of electron-electron interactions near the point contact.

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 systems are discussed.

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 edges. Analytic results are obtained. The values of the fractional quasiparticle charges obtained agree with the predictions of previous theories in the incompressible regions of the 2DEG where those theories apply. In the compressible regions the magnitudes of the quasiparticle charges vary with position. Since Johnson-Nyquist noise arises from the compressible regions, it is due to quasiparticles whose charges differ from the simple fractions of $e$ that apply in the incompressible regions. Never the less, the Nyquist noise formula $S=4{k_B}T G$ is obeyed on fractional quantum Hall plateaus. Some implications for the interpretation of recent shot noise measurements in the fractional quantum Hall regime are briefly discussed.

Bulk charge distributions on integer and fractional quantum Hall plateaus

We discuss the charge distributions across the bulk of a two-dimensional electron-gas system that is on an integer or fractional quantum Hall plateau. Our analysis is based on a relation, derived from the long-wavelength limit of the bulk density-density response function, between the induced charge and leading derivatives of a slowly varying Hall potential. We use the Wiener-Hopf method to solve the coupled response and Poisson equations. Unlike the integer case, treated in previous work, the induced charge in the fractional case can alternate in sign.

Scaling in the metal-insulator transition of the fractional quantum Hall effect

We study the magnetoresistance of a high-mobility two-dimensional electron gas at mK temperatures. In particular, the metal-insulator transitions between two adjacent fractional quantum Hall states ( 3 5 – 2 3 ) and between an integral and a fractional quantum Hall plateau ( 2 3−1 , 1−4 3 and 5 3−2 ) are investigated. We obtain a scaling behaviour of the width Δ B of the transition region as a function of the temperature T: ΔB ∝ T k , for T below a characteristic temperature T c. Within the experimental error, the exponent κ is the same for all the transitions and is found to be in the range from 0.40 to 0.45. These findings agree with the results of recent theoretical studies. We study the effect of tilted magnetic fields on the scaling behaviour and find a considerable influence of the electronic spin.

Novel quantum hall phenomena in arrays of quantum dots

A theory of two-dimensional arrays of coupled quantum dots in transverse magnetic fields is described. These systems are expected to exhibit exotic Hofstadter-like spectral and transport properties at modest magnetic fields ≥1 Tesla. They are shown to support intricate spectra of normal and “counter-rotating” magnetic edge states. The edge states are predicted to give rise to positive, negative and fractional quantum Hall plateaus in ballistic arrays coupled to ideal reservoirs. The fractions differ in value and origin from the usual fractional quantum Hall effect. In non-ballistic, macroscopic systems we predict integer positive and negative quantum Hall plateaus only, as in earlier theories of electrons in periodic 2D systems. This is understood in terms of “directed localization”, a generalization of Anderson localization to disordered waveguides supporting different numbers of modes propagating in opposite directions. The sample quality requirements for observing these effects are found to be very stringent.

Pinning and conductivity of a two-dimensional charge-density wave in a strong magnetic field.

We investigate the dynamics of a two-dimensional electron system in a high magnetic field in the Wigner-crystalline regime where charge-density-wave correlations extend over a distance large compared with the interelectronic spacing. We determine the effects of weak disorder and of screening by uncondensed carriers of the internal electric fields produced by crystal deformation. We show, in agreement with previous work, that in the presence of disorder a dispersing, albeit inhomogeneously broadened mode exists even at wavelengths long compared with the positional correlation length. We obtain expressions for the line shape of the mode in terms of properties of the disorder. We compare our results to presently available data, concluding that present observations imply a correlation length of order one lattice constant at very large fields. However, threshold field measurements at smaller fields near the \ensuremath{\nu}=1/5 fractional quantum Hall plateau imply much larger correlation lengths, suggesting an anomalous field dependence of system properties.

Observation of the i=1/2 fractional quantum Hall plateau in AlGaAs/GaAs/AlGaAs selectively doped double heterostructures

An inverted and a normal GaAs/AlGaAs interface grown back to back in a socially selectively doped double heterostructure (SDDH) has been studied in magnetic fields up to 12 T and at temperatures down to 0.3 K. The longitudinal resistance goes to zero at the minima of the Shubnikov-de Haas oscillations. The Hall resistivity is found to exhibit the quantum Hall effect. By etching the surface of the double heterostructure wafer the authors create an imbalance in the density of electrons in the two parallel two-dimensional electronic sheets. Although in this way they create only a modest change in the electron densities, they observe a significant change in the Shubnikov-de Haas oscillations, which can be interpreted as a beat between the oscillations of two electron layers with different densities. At the same time they observe a significant variation of the width of the quantum Hall steps. The most astonishing feature of the results is a clear quantum Hall plateau at 1/2 filling in each of the two parallel layers observed at temperatures below 1 K and at a magnetic field about 10 T. Weak localisation was also studied and such experiments are consistent with two parallel and independent two-dimensional electronic layers.