The fractional quantum Hall effect, where plateaus in the Hall resistance at values of h/nue2 coexist with zeros in the longitudinal resistance, results from electron correlations in two dimensions ...under a strong magnetic field. (Here h is Planck's constant, nu the filling factor and e the electron charge.) Current flows along the sample edges and is carried by charged excitations (quasiparticles) whose charge is a fraction of the electron charge. Although earlier research concentrated on odd denominator fractional values of nu, the observation of the even denominator nu = 5/2 state sparked much interest. This state is conjectured to be characterized by quasiparticles of charge e/4, whose statistics are 'non-abelian'-in other words, interchanging two quasiparticles may modify the state of the system into a different one, rather than just adding a phase as is the case for fermions or bosons. As such, these quasiparticles may be useful for the construction of a topological quantum computer. Here we report data on shot noise generated by partitioning edge currents in the nu = 5/2 state, consistent with the charge of the quasiparticle being e/4, and inconsistent with other possible values, such as e/2 and e. Although this finding does not prove the non-abelian nature of the nu = 5/2 state, it is the first step towards a full understanding of these new fractional charges.
Electron pairing is a rare phenomenon appearing only in a few unique physical systems; for example, superconductors and Kondo-correlated quantum dots. Here, we report on an unexpected electron ...pairing in the integer quantum Hall effect regime. The pairing takes place within an interfering edge channel in an electronic Fabry-Perot interferometer at a wide range of bulk filling factors, between 2 and 5. We report on three main observations: high-visibility Aharonov-Bohm conductance oscillations with magnetic flux periodicity equal to half the magnetic flux quantum; an interfering quasiparticle charge equal to twice the elementary electron charge as revealed by quantum shot noise measurements, and full dephasing of the pairs' interference by induced dephasing of the adjacent inner edge channel-a manifestation of inter-channel entanglement. Although this pairing phenomenon clearly results from inter-channel interaction, the exact mechanism that leads to electron-electron attraction within a single edge channel is not clear. We believe that substantial efforts are needed in order to clarify these intriguing and unexpected findings.
Studies of electronic interferometers, based on edge-channel transport in the quantum Hall effect regime, have been stimulated by the search for evidence of abelian and non-abelian anyonic statistics ...of fractional charges. In particular, the electronic Fabry-Pérot interferometer has been found to be Coulomb dominated, thus masking coherent Aharonov-Bohm interference patterns: the flux trapped within the interferometer remains unchanged as the applied magnetic field is varied, barring unobservable modulations of the interference area. Here we report on conductance measurements indicative of the interferometer's area 'breathing' with the variation of the magnetic field, associated with observable (a fraction of a flux quantum) variations of the trapped flux. This is the result of partial (controlled) screening of Coulomb interactions. Our results introduce a novel experimental tool for probing anyonic statistics.
Quantum critical systems derive their finite-temperature properties from the influence of a zero-temperature quantum phase transition. The paradigm is essential for understanding unconventional ...high-Tc superconductors and the non-Fermi liquid properties of heavy fermion compounds. However, the microscopic origins of quantum phase transitions in complex materials are often debated. Here we demonstrate experimentally, with support from numerical renormalization group calculations, a universal crossover from quantum critical non-Fermi liquid behaviour to distinct Fermi liquid ground states in a highly controllable quantum dot device. Our device realizes the non-Fermi liquid two-channel Kondo state, based on a spin-1/2 impurity exchange-coupled equally to two independent electronic reservoirs. On detuning the exchange couplings we observe the Fermi liquid scale T*, at energies below which the spin is screened conventionally by the more strongly coupled channel. We extract a quadratic dependence of T* on gate voltage close to criticality, and validate an asymptotically exact description of the universal crossover between strongly correlated non-Fermi liquid and Fermi liquid states.
The quantum Hall effect takes place in a two-dimensional electron gas under a strong magnetic field and involves current flow along the edges of the sample. For some particle-hole conjugate states of ...the fractional regime (for example, with fillings between 1/2 and 1 of the lowest Landau level), early predictions suggested the presence of counter-propagating edge currents in addition to the expected ones. When this did not agree with the measured conductance, it was suggested that disorder and interactions will lead to counter-propagating modes that carry only energy--the so called neutral modes. In addition, a neutral upstream mode (the Majorana mode) was expected for selected wavefunctions proposed for the even-denominator filling 5/2. Here we report the direct observation of counter-propagating neutral modes for fillings of 2/3, 3/5 and 5/2. The basis of our approach is that, if such modes impinge on a narrow constriction, the neutral quasiparticles will be partly reflected and fragmented into charge carriers, which can be detected through shot noise measurements. We find that the resultant shot noise is proportional to the injected current. Moreover, when we simultaneously inject a charge mode, the presence of the neutral mode was found to significantly affect the Fano factor and the temperature of the backscattered charge mode. In particular, such observations for filling 5/2 may single out the non-Abelian wavefunctions for the state.
We experimentally investigate the charge (isospin) frustration induced by a geometrical symmetry in a triangular triple quantum dot. We observe the ground-state charge configurations of sixfold ...degeneracy, the manifestation of the frustration. The frustration results in omnidirectional charge transport, and it is accompanied by nearby nontrivial triple degenerate states in the charge stability diagram. The findings agree with a capacitive interaction model. We also observe unusual transport by the frustration, which might be related to elastic cotunneling and the interference of trajectories through the dot. This work demonstrates a unique way of studying geometrical frustration in a controllable way.
Very much like the ubiquitous quantum interference of a single particle with itself, quantum interference of two independent, but indistinguishable, particles is also possible. For a single particle, ...the interference is between the amplitudes of the particle's wavefunctions, whereas the interference between two particles is a direct result of quantum exchange statistics. Such interference is observed only in the joint probability of finding the particles in two separated detectors, after they were injected from two spatially separated and independent sources. Experimental realizations of two-particle interferometers have been proposed; in these proposals it was shown that such correlations are a direct signature of quantum entanglement between the spatial degrees of freedom of the two particles ('orbital entanglement'), even though they do not interact with each other. In optics, experiments using indistinguishable pairs of photons encountered difficulties in generating pairs of independent photons and synchronizing their arrival times; thus they have concentrated on detecting bunching of photons (bosons) by coincidence measurements. Similar experiments with electrons are rather scarce. Cross-correlation measurements between partitioned currents, emanating from one source, yielded similar information to that obtained from auto-correlation (shot noise) measurements. The proposal of ref. 3 is an electronic analogue to the historical Hanbury Brown and Twiss experiment with classical light. It is based on the electronic Mach-Zehnder interferometer that uses edge channels in the quantum Hall effect regime. Here we implement such an interferometer. We partitioned two independent and mutually incoherent electron beams into two trajectories, so that the combined four trajectories enclosed an Aharonov-Bohm flux. Although individual currents and their fluctuations (shot noise measured by auto-correlation) were found to be independent of the Aharonov-Bohm flux, the cross-correlation between current fluctuations at two opposite points across the device exhibited strong Aharonov-Bohm oscillations, suggesting orbital entanglement between the two electron beams.
Double-slit electron interferometers fabricated in high mobility two-dimensional electron gases are powerful tools for studying coherent wave-like phenomena in mesoscopic systems. However, they ...suffer from low visibility of the interference patterns due to the many channels present in each slit, and from poor sensitivity to small currents due to their open geometry. Moreover, these interferometers do not function in high magnetic fields-such as those required to enter the quantum Hall effect regime-as the field destroys the symmetry between left and right slits. Here we report the fabrication and operation of a single-channel, two-path electron interferometer that functions in a high magnetic field. This device is the first electronic analogue of the optical Mach-Zehnder interferometer, and opens the way to measuring interference of quasiparticles with fractional charges. On the basis of measurements of single edge state and closed geometry transport in the quantum Hall effect regime, we find that the interferometer is highly sensitive and exhibits very high visibility (62%). However, the interference pattern decays precipitously with increasing electron temperature or energy. Although the origin of this dephasing is unclear, we show, via shot-noise measurements, that it is not a decoherence process that results from inelastic scattering events.
We report the observation of an unpredictable behavior of a simple, two-path, electron interferometer. Utilizing an electronic analog of the well-known optical Mach-Zehnder interferometer, with ...current carrying edge channels in the quantum Hall effect regime, we measured high contrast Aharonov-Bohm (AB) oscillations. Surprisingly, the amplitude of the oscillations varied with energy in a lobe fashion, namely, with distinct maxima and zeros (namely, no AB oscillations) in between. Moreover, the phase of the AB oscillations was constant throughout each lobe period but slipped abruptly by pi at each zero. The periodicity of the lobes defines a new energy scale, which may be a general characteristic of quantum coherence of interfering electrons.
Determination of the path taken by a quantum particle leads to a suppression of interference and to a classical behavior. We employ here a quantum "which path" detector to perform accurate path ...determination in a two-path Mach-Zehnder electron interferometer, leading to full suppression of the interference. Following the dephasing process we recover the interference by measuring the cross correlation between the interferometer and detector currents. Under our measurement conditions every interfering electron is dephased by approximately a single electron in the detector-leading to mutual entanglement of approximately single pairs of electrons.
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