Interactions suppress quasiparticle tunneling at Hall bar constrictions

Observation of the scaling dimension of fractional quantum Hall anyons

Unconventional quasiparticles emerging in the fractional quantum Hall regime1,2 present the challenge of observing their exotic properties unambiguously. Although the fractional charge of quasiparticles has been demonstrated for nearly three decades3-5, the first convincing evidence of their anyonic quantum statistics has only recently been obtained6,7 and, so far, the so-called scaling dimension that determines the propagation dynamics of the quasiparticles remains elusive. In particular, although the nonlinearity of the tunnelling quasiparticle current should reveal their scaling dimension, the measurements fail to match theory, arguably because this observable is not robust to non-universal complications8-12. Here we expose the scaling dimension from the thermal noise to shot noise crossover and observe an agreement with expectations. Measurements are fitted to the predicted finite-temperature expression involving both the scaling dimension of the quasiparticles and their charge12,13, in contrast to previous charge investigations focusing on the high-bias shot-noise regime14. A systematic analysis, repeated on several constrictions and experimental conditions, consistently matches the theoretical scaling dimensions for the fractional quasiparticles emerging at filling factors ν = 1/3, 2/5 and 2/3. This establishes a central property of fractional quantum Hall anyons and demonstrates a powerful and complementary window into exotic quasiparticles.

Anyon Statistics through Conductance Measurements of Time-Domain Interferometry

We propose a method to extract the mutual exchange statistics of the anyonic excitations of a general Abelian fractional quantum Hall state, by comparing the tunneling characteristics of a quantum point contact in two different experimental conditions. In the first, the tunneling current between two edges at different chemical potentials is measured. In the second, one of these edges is strongly diluted by an earlier point contact. We describe the case of the dilute beam in terms of a time-domain interferometer between the anyons flowing along the edge and quasiparticle-quasihole excitations created at the tunneling quantum point contact. In both cases, temperature is kept large, such that the measured current is given to linear response. Remarkably, our proposal does not require the measurement of current correlations, and allows us to carefully separate effects of the fractional charge and statistics from effects of intra- and interedge interactions.

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.

Stabilization of the Particle-Hole Pfaffian Order by Landau-Level Mixing and Impurities That Break Particle-Hole Symmetry

Numerical results suggest that the quantum Hall effect at ν=5/2 is described by the Pfaffian or anti-Pfaffian state in the absence of disorder and Landau-level mixing. Those states are incompatible with the observed transport properties of GaAs heterostructures, where disorder and Landau-level mixing are strong. We show that the recent proposal of a particle-hole (PH)-Pfaffian topological order by Son is consistent with all experiments. The absence of particle-hole symmetry at ν=5/2 is not an obstacle to the existence of the PH-Pfaffian order since the order is robust to symmetry breaking.

Metal-insulator transition in the quasi-one-dimensional transport of fractional quantum Hall states

We investigate edge state transmission in quantum point contacts (QPCs) in the fractional quantum-Hall regime, finding behavior reminiscent of a metal-insulator transition. The transition is suggested by an unusual behavior of the differential conductance in the fractional-quantum-Hall regime, and by the presence of a fixed point and universal scaling in the temperature dependence of the linear conductance. Noting that the 0.7 feature evolves continuously into a last fractional plateau at high magnetic fields, we suggest that this still unresolved feature may itself be viewed as a manifestation of a local, microscopic, metal-insulator transition.

Anomalous charge tunneling in fractional quantum Hall edge states at a filling factor ν=5/2

We explain effective charge anomalies recently observed for fractional quantum Hall edge states at ν=5/2 [M. Dolev, Y. Gross, Y. C. Chung, M. Heiblum, V. Umansky, and D. Mahalu, Phys. Rev. B 81, 161303(R) (2010)]. The experimental data of differential conductance and excess noise are fitted, using the anti-Pfaffian model, by properly taking into account renormalizations of the Luttinger parameters induced by the coupling of the system with an intrinsic 1/f noise. We demonstrate that a peculiar agglomerate excitation with charge e/2, double the expected e/4 charge, dominates the transport properties at low energies.

AC conductivity of a quantum Hall line junction

We present a microscopic model for calculating the AC conductivity of a finite length line junction made up of two counter- or co-propagating single mode quantum Hall edges with possibly different filling fractions. The effect of density-density interactions and a local tunneling conductance (σ) between the two edges is considered. Assuming that σ is independent of the frequency ω, we derive expressions for the AC conductivity as a function of ω, the length of the line junction and other parameters of the system. We reproduce the results of Sen and Agarwal (2008 Phys. Rev. B 78 085430) in the DC limit ([Formula: see text]), and generalize those results for an interacting system. As a function of ω, the AC conductivity shows significant oscillations if σ is small; the oscillations become less prominent as σ increases. A renormalization group analysis shows that the system may be in a metallic or an insulating phase depending on the strength of the interactions. We discuss the experimental implications of this for the behavior of the AC conductivity at low temperatures.

Relevance of multiple quasiparticle tunneling between edge states at nu=p/(2np+1)

We present an explanation for the anomalous behavior in tunneling conductance and noise through a point contact between edge states in the Jain series nu=p/(2np+1), for extremely weak backscattering and low temperatures [Y. C. Chung, M. Heiblum, and V. Umansky, Phys. Rev. Lett. 91, 216804 (2003)10.1103/PhysRevLett.91.216804]. We consider edge states with neutral modes propagating at finite velocity, and we show that the activation of their dynamics causes the unexpected change in the temperature power law of the conductance. Even more importantly, we demonstrate that multiple-quasiparticle tunneling at low energies becomes the most relevant process. This result will be used to explain the experimental data on current noise where tunneling particles have a charge that can reach p times the single-quasiparticle charge. In this Letter, we analyze the conductance and the shot noise to substantiate quantitatively the proposed scenario.

Metal-insulator transition tuned by external gates in Hall systems with constrictions

The nature of a metal-insulator transition tuned by external gates in quantum Hall systems with point constrictions, as reported in recent experiments [S. Roddaro, Phys. Rev. Lett. 95, 156804 (2005)10.1103/PhysRevLett.95.156804], is examined. We attribute this phenomenon to a splitting of the integer edge into conducting and insulating stripes, the latter wide enough to allow for the stability of the edge structure. Interchannel impurity scattering and interchannel Coulomb interactions do not destabilize this picture.

Particle-hole symmetric Luttinger liquids in a quantum Hall circuit

We report current transmission data through a split-gate constriction fabricated onto a two-dimensional electron system in the integer quantum Hall (QH) regime. Split-gate biasing drives interedge backscattering and is shown to lead to suppressed or enhanced transmission, in marked contrast to the expected linear Fermi-liquid behavior. This evolution is described in terms of particle-hole symmetry and allows us to conclude that an unexpected class of gate-controlled particle-hole-symmetric chiral Luttinger liquids (CLLs) can exist at the edges of our QH circuit. These results highlight the role of particle-hole symmetry on the properties of CLL edge states.

Temperature dependence of the tunneling amplitude between quantum hall edges

Recent experiments have studied the tunneling current between the edges of a fractional quantum Hall liquid as a function of temperature and voltage. The results of the experiment are puzzling because at "high" temperature (600-900 mK) the behavior of the tunneling conductance is consistent with the theory of tunneling between chiral Luttinger liquids, but at low temperature it strongly deviates from that prediction dropping to zero with decreasing temperature. In this Letter we suggest a possible explanation of this behavior in terms of the strong temperature dependence of the tunneling amplitude.