M. Heiblum

Analysis of curved optical waveguides by conformal transformation

The method of conformal transformations is applied to the analysis of waveguide bends. Equivalent structures are obtained that permit solution by traditional methods of optical waveguide analysis. Losses associated with both curvature and with the transition from straight to curved guides are discussed and simple first-order expressions that describe the dependence of the losses on waveguide parameters are derived.

Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions

Majorana fermions are the only fermionic particles that are expected to be their own antiparticles. While elementary particles of the Majorana type were not identified yet, quasi-particles with Majorana like properties, born from interacting electrons in the solid, were predicted to exist. Here, we present thorough experimental studies, backed by numerical simulations, of a system composed of an aluminum superconductor in proximity to an indium arsenide nanowire, with the latter possessing strong spin-orbit coupling. An induced 1d topological superconductor - supporting Majorana fermions at both ends - is expected to form. We concentrate on the characteristics of a distinct zero bias conductance peak (ZBP), and its splitting in energy, both appearing only with a small magnetic field applied along the wire. The ZBP was found to be robustly tied to the Fermi energy over a wide range of system parameters. While not providing a definite proof of a Majorana state, the presented data and the simulations support strongly its existence.

An electronic Mach-Zehnder interferometer.

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.

Dephasing in electron interference by a 'which-path'detector

Wave–particle duality, as manifest in the two-slit experiment, provides perhaps the most vivid illustration of Bohrs complementarity principle: wave-like behaviour (interference) occurs only when the different possible paths a particle can take are indistinguishable, even in principle. The introduction of a which-path (welcher Weg) detector for determining the actual path taken by the particle inevitably involved coupling the particle to a measuring environment, which in turn results in dephasing (suppression of interference). In other words, simultaneous observations of wave and particle behaviour is prohibited. Such a manifestation of the complementarity principle was demonstrated recently using a pair of correlated photons, with measurement of one photon being used to determine the path taken by the other and so prevent single-photon interference. Here we report the dephasing effects of a which-path detector on electrons traversing a double-path interferometer. We find that by varying the sensitivity of the detector we can affect the visibility of the oscillatory interference signal, thereby verifying the complementarity principle for fermions.

Method for suppression of stacking faults in Wurtzite III-V nanowires.

The growth of wurtzite GaAs and InAs nanowires with diameters of a few tens of nanometers with negligible intermixing of zinc blende stacking is reported. The suppression of the number of stacking faults was obtained by a procedure within the vapor-liquid-solid growth, which exploits the theoretical result that nanowires of small diameter ( approximately 10 nm) adopt purely wurtzite structure and are observed to thicken (via lateral growth) once the axial growth exceeds a certain length.

Characteristics of AuGeNi ohmic contacts to GaAs

Abstract We have studied AuGeNi ohmic contacts to n-type MBE grown GaAs epitaxial-layer with doping in the (1016−1019) cm−3 range, and found several new effects: (a) Contact resistivity exhibit a weak dependence on carrier concentration (much weaker than 1/ND depencence); (b) We find evidence for a high resistivity layer under the contact at least several thousands angstroms deep, which dominate the contact resistance in most cases; (c) We find a peripheral zone around the contact, about 1 μm wide which differs chemically from the GaAs epi-layer; (d) SIMS analysis reveals a deep diffusion into the GaAs of Ni and Ge; (e) Correlation between density of GeNi clusters in the contact and the contact resistivity are found; (f) Temperature measurements justify that tunneling is responsible for the ohmic contact. We discuss also the validity of the transmission line method and the commonly accepted model of the contact.

Observation of a quarter of an electron charge at the |[ngr]| = 5/2 quantum Hall state

The fractional quantum Hall effect, where plateaus in the Hall resistance at values of 2 / h e ν coexist with zeros in the longitudinal resistance, results from electron correlations in two dimensions under a strong magnetic field. Current flows along the edges carried by charged excitations (quasi particles) whose charge is a fraction of the electron charge. While earlier research concentrated on odd denominator fractional values of ν, the observation of the even denominator ν=5/2 state sparked a vast interest. This state is conjectured to be characterized by quasiparticles of charge e/4, whose statistics is “non-abelian”. In other words, interchanging of two quasi particles may modify the state of the system to an orthogonal one, and does not just add a phase as in for fermions or bosons. As such, these quasiparticles may be useful for the construction of a topological quantum computer. Here we report data of shot noise generated by partitioning edge currents in the ν=5/2 state, consistent with the charge of the quasiparticle being e/4, and inconsistent with other potentially possible values, such as e/2 and e. While not proving the ‘non-abelian’ nature of the ν=5/2 state, this observation is the first step toward a full understanding of these new fractional charges.The fractional quantum Hall effect, where plateaus in the Hall resistance at values of h/νe2 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, ν 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 ν, the observation of the even denominator ν = 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 ν = 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 ν = 5/2 state, it is the first step towards a full understanding of these new fractional charges.

Phase evolution in a Kondo-correlated system.

We measured the phase evolution of electrons as they traverse a quantum dot (QD) formed in a two-dimensional electron gas that serves as a localized spin. The traversal phase, determined by embedding the QD in a double path electron interferometer and measuring the quantum interference of the electron wave functions manifested by conductance oscillation as a function of a weak magnetic field, evolved by pi radians, a range twice as large as theoretically predicted. As the correlation weakened, a gradual transition to the familiar phase evolution of a QD was observed. The specific phase evolution observed is highly sensitive to the onset of Kondo correlation, possibly serving as an alternative fingerprint of the Kondo effect.

Interference between two indistinguishable electrons from independent sources

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.

Tunneling hot-electron transfer amplifier: a hot-electron GaAs device with current gain

Tunneling hot‐electron transfer amplifier (THETA) devices, based on GaAs‐AlGaAs heterojunctions, were fabricated and tested. Hot‐electron transfer (α) through a 1100‐A base in excess of 70% was found at 4.2 K. This resulted in a corresponding current gain ( β) in a common emitter configuration of about 2.3. In the temperature range of 4.2–80 K and under constant biasing conditions, α was nearly temperature independent. Electron energy distributions for motion normal to the layers and electron total energy loss while traversing the device were estimated. Typical widths of the energy distributions were less than 200 meV, and both widths and energy peak positions were only slightly dependent on temperature and initial injection energy.