RECENT RESULTS

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

Anindya Das, Yuval Ronen, Yonatan Most, Yuval Oreg, Moty Heiblum and Hadas Shtrikman

Majorana fermions are the only fermionic particles that are expected to be their own antiparticles. Although elementary
particles of the Majorana type have not been identified yet, quasi-particles with Majorana-like properties, born from interacting
electrons in the solid, have been predicted to exist.

Here, we present thorough experimental studies, backed by numerical
simulations, of a system composed of an aluminium superconductor in proximity to an indium arsenide nanowire, with the
latter possessing strong spin–orbit coupling and Zeeman splitting. An induced one-dimensional topological superconductor,
supporting Majorana fermions at both ends, is expected to form. We concentrate on the characteristics of a distinct zero-bias
conductance peak and its splitting in energy—both appearing only with a small magnetic field applied along the wire. The
zero-bias conductance peak was found to be robustly tied to the Fermi energy over a wide range of system parameters. Although
not providing definite proof of a Majorana state, the presented data and the simulations support its existence.

Reference :

Nature Physics 8, 887 (2012)
High-efficiency Cooper pair splitting demonstrated by two-particle conductance resonance and positive noise cross-correlation

Anindya Das, Yuval Ronen, Moty Heiblum, Diana Mahalu, Andrey V. Kretinin, and Hadas Shtrikman

Entanglement is at the heart of the Einstein-Podolsky-Rosen paradox, where the non-locality
is a necessary ingredient. Cooper pairs in superconductors can be split adiabatically, thus
forming entangled electrons.

Here, we fabricate such an electron splitter by contacting an aluminium superconductor strip at the centre of a suspended InAs nanowire.
The nanowire is terminated at both ends with two normal metallic drains. Dividing each half of the nanowire
by a gate-induced Coulomb blockaded quantum dot strongly impeds the flow of Cooper pairs
due to the large charging energy, while still permitting passage of single electrons.
We provide conclusive evidence of extremely high efficiency Cooper pair splitting via observing
positive two-particle correlations of the conductance and the shot noise of the split electrons
in the two opposite drains of the nanowire. Moreover, the actual charge of the injected
quasiparticles is verified by shot noise measurements.

Reference :

Nat. Comm. 3, 1165 (2012)
Observation of Neutral Modes in the Fractional Quantum Hall Regime

A. Bid, O. Nissim, H. Inoue, M. Heiblum, C. L. Kane, V. Umansky, and D. Mahalu

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.

Reference :

Nature 466, 585 (2010)
Observation of a quarter of an electron charge at the v=5/2 quantum Hall state

M. Dolev, M. Heiblum, V. Umansky, Ady Stern & D. Mahalu

The fractional quantum Hall effect, where plateaus in the Hall resistance at values of h/ve

2 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, v 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 v, the observation of the even denominator v=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 v=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 v=5/2 state, it is the first step towards a full understanding of these new fractional charges.

Reference :

Nature 452, 829 (2008)
Interference between two indistinguishable electrons from independent sources

I. Neder, N. Ofek, Y. Chung, M. Heiblum, D. Mahalu & V. Umansky

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.

Reference :

Nature 448, 333 (2007)
Entanglement, Dephasing and Phase Recovery via Cross-Correlation Measurements of Electrons

I. Neder, M. Heiblum, D. Mahalu and V. Umansky

Coherence, leading to interference of quantum particles, is possible only when the path the particles choose cannot be determined - even in principle. Determination of the chosen path leads to suppression of the interference – ‘dephasing’ - causing the particles to behave classically.

For a macroscopic object this happens due to unavoidable interactions with the environment. A thorough understanding of such quantum to classical transition is of fundamental importance, especially with the emergence of quantum information research. Experiments, where path detection was not accurate enough, leading thus only to weak dephasing, was already performed before in mesoscopic systems. Here, however, we employ a sensitive quantum ‘which path’ detector to perform an accurate path determination in a two-path electron-interferometer, leading to full suppression of the interference. We then demonstrate that phase information is not lost, but can be recovered from the combined system: interferometer & detector.
While each alone is phase insensitive, measuring the combined shot noise of both currents exhibits the original interference oscillations. This is a direct result of the cross-correlation term of the two current fluctuations (being part of the shot noise). Our present work resembles previous experiments where the two quantum systems were two parametrically - down converted - entangled photons. Moreover, in our experiment, approximately a single electron in the detector fully dephases an electron in the interferometer, leading to entanglement of single pairs of electrons.

Reference :

Phys. Rev. Lett. 98, 036803 (2007)
Coherence and Phase in an Electronic Mach-Zehnder Interferometer: An Unexpected Behavior of Interfering Electrons

I. Neder, M. Heiblum, Y. Levinson, D. Mahalu, and V. Umansky

We report the observation of an unpredicted behavior of interfering 2D electrons in the integer quantum Hall effect (IQHE) regime via a utilization of an electronic analog of the well-known Mach-Zehnder interferometer (MZI). The beauty of this experiment lies in the simplicity of two path interference.

Electrons that travel the two paths via edge channels, feel only the edge potential and the strong magnetic field; both typical in the IQHE regime. Yet, the interference of these electrons via the Aharonov-Bohm (AB) effect, behaves surprisingly in a most uncommon way. We found, at filling factors 1 and 2, high visibility interference oscillations, which were strongly modulated by a lobe-type structure as we increased the electron injection voltage.
The visibility went through a few maxima and zeros in between, with the phase of the AB oscillations staying constant throughout each lobe and slipping abruptly by pi at each zero. The lobe pattern and the 'stick-slip' behavior of the phase were insensitive to details of the interferometer structure; but highly sensitive to magnetic field. The observed periodicity defines a ‘new energy scale’ with an unclear origin. The phase rigidity, on the other hand, is surprising since Onsager relations are not relevant here.

Reference :

Phys. Rev. Lett. 96, 016804 (2006)
Crossover from ‘mesoscopic’ to ‘universal’ phase for electron transmission in quantum dots

M. Avinun-Kalish, M. Heiblum, O. Zarchin, D. Mahalu and V. Umansky

Measuring phase in coherent electron systems (mesoscopic systems) provides ample information not easily revealed by ubiquitous conductance measurements. Such experiments, recently employed to measure the transmission phase of many-electron quantum dots (QDs), demonstrated a universal phase evolution independent of dot size, shape, and occupancy. Explicitly, in Coulomb blockaded QDs, the transmission phase has been shown to increase monotonically by pi throughout each conductance peak (due to an electron entering the dot); thereafter, in the conductance valleys it returned sharply to its base value.

Expected mesoscopic features in the phase such as spin degeneracy or exchange effects were never observed. Presently, there is no satisfactory explanation for this unexpected behavior where the QD seems always to return to the same ground state phase! Here we report on a new set of phase measurements conducted on dots with occupation varying from a single to twenty electrons. The measurements are performed on a QD embedded in one arm of a two path electron interferometer. An electron counter is placed in close proximity to the QD.
Unlike the universal phase behavior of larger dots the phase evolution in these small dots exhibits a mesoscopic type behavior when they are occupied with less then some ten electrons. Features in the phase indicate spin degeneracy and exchange effects that depend on the exact shape and occupation of the dots. As the number of electrons increases from around ten to some fifteen electrons the phase evolves through a transition region, later (for N>15) collapsing to the familiar universal behavior with its characteristic repetitive behavior.
This provides clear evidence that the behavior of QDs can not be fully accounted by the ubiquitous single particle model. As in previous phase measurements, the phase proves again to be far more sensitive than the conductance to intricate physical effects.

Reference :

Nature 436, 529 (2005)