Measuring statistics-induced entanglement entropy with a Hong-Ou-Mandel interferometer.

Despite its ubiquity in quantum computation and quantum information, a universally applicable definition of quantum entanglement remains elusive. The challenge is further accentuated when entanglement is associated with other key themes, e.g.

Anomalous Aharonov-Bohm Interference in the Presence of Edge Reconstruction.

Interferometry is a vital tool for studying fundamental features in the quantum Hall effect. For instance, Aharonov-Bohm interference in a quantum Hall interferometer can probe the wave-particle duality of electrons and quasiparticles. Here, we report an unusual Aharonov-Bohm interference of the outermost edge mode in a quantum Hall Fabry-Pérot interferometer, whose Coulomb interactions were suppressed with a grounded drain in the interior bulk of the interferometer.

Heat conductance of the quantum Hall bulk.

The quantum Hall effect is a prototypical realization of a topological state of matter. It emerges from a subtle interplay between topology, interactions and disorder. The disorder enables the formation of localized states in the bulk that stabilize the quantum Hall states with respect to the magnetic field and carrier density.

Electron Pairing of Interfering Interface-Based Edge Modes.

The remarkable Cooper-like pairing phenomenon in the Aharonov-Bohm interference of a Fabry-Perot interferometer-operating in the integer quantum Hall regime-remains baffling. Here, we report the interference of paired electrons employing "interface edge modes." These modes are born at the interface between the bulk of the Fabry-Perot interferometer and an outer gated region tuned to a lower filling factor.

Isolated ballistic non-abelian interface channel.

The topological order of a quantum Hall state is mirrored by the gapless edge modes owing to bulk-edge correspondence. The state at the filling of ν = 5/2, predicted to host non-abelian anyons, supports a variety of edge modes (integer, fractional, neutral). To ensure thermal equilibration between the edge modes and thus accurately determine the state's nature, it is advantageous to isolate the fractional channel (1/2 and neutral modes).

Distinguishing between non-abelian topological orders in a quantum Hall system.

Quantum Hall states can harbor exotic quantum phases. The nature of these states is reflected in the gapless edge modes owing to “bulk-edge” correspondence. The most studied putative non-abelian state is the spin-polarized filling factor (ν) = 5/2, which permits different topological orders that can be abelian or non-abelian.

Energy Relaxation in Edge Modes in the Quantum Hall Effect.

Studies of energy flow in quantum systems complement the information provided by common conductance measurements. The quantum limit of heat flow in one-dimensional ballistic modes was predicted, and experimentally demonstrated, to have a universal value for bosons, fermions, and fractionally charged anyons. A fraction of this value is expected in non-Abelian states; harboring counterpropagating edge modes.

Melting of Interference in the Fractional Quantum Hall Effect: Appearance of Neutral Modes.

We attempted to measure interference of the outer edge mode in the fractional quantum hall regime with an electronic Mach-zehnder interferometer. The visibility of the interferometer wore off as we approached ν_{B}=1 and the transmission of the quantum point contacts (QPCs) of the interferometer simultaneously developed a v=1/3 conductance plateau accompanied by shot noise. The appearance of shot noise on this plateau indicates the appearance of nontopological neutral modes resulting from edge reconstruction.

Concomitant opening of a bulk-gap with an emerging possible Majorana zero mode.

Majorana quasiparticles are generally detected in a 1D topological superconductor by tunneling electrons into its edge, with an emergent zero-bias conductance peak (ZBCP). However, such a ZBCP can also result from other mechanisms, hence, additional verifications are required. Since the emergence of a Majorana must be accompanied by an opening of a topological gap in the bulk, two simultaneous measurements are performed: one in the bulk and another at the edge of a 1D InAs nanowire coated with epitaxial aluminum.

Synthesizing a ν=2/3 fractional quantum Hall effect edge state from counter-propagating ν=1 and ν=1/3 states.

Topological edge-reconstruction occurs in hole-conjugate states of the fractional quantum Hall effect. The frequently studied filling factor, ν = 2/3, was originally proposed to harbor two counter-propagating modes: a downstream v = 1 and an upstream v = 1/3. However, charge equilibration between these two modes always led to an observed downstream v = 2/3 charge mode accompanied by an upstream neutral mode.

Counter-propagating charge transport in the quantum Hall effect regime.

The quantum Hall effect, observed in a two-dimensional (2D) electron gas subjected to a perpendicular magnetic field, imposes a 1D-like chiral, downstream, transport of charge carriers along the sample edges. Although this picture remains valid for electrons and Laughlin's fractional quasiparticles, it no longer holds for quasiparticles in the so-called hole-conjugate states. These states are expected, when disorder and interactions are weak, to harbor upstream charge modes.

Author Correction: Observation of half-integer thermal Hall conductance.

In this Article, the publication details for references 33, 34 and 40 have been corrected online.

Theory of Disorder-Induced Half-Integer Thermal Hall Conductance.

The thermal Hall conductance in the half-filled first Landau level was recently measured to take the quantized noninteger value κ_{xy}=5/2 (in units of temperature times π^{2}k_{B}^{2}/3h), which indicates a non-Abelian phase of matter. Such exotic states have long been predicted to arise at this filling factor, but the measured value disagrees with numerical studies, which predict κ_{xy}=3/2 or 7/2. We resolve this contradiction by invoking the disorder-induced formation of mesoscopic puddles with locally κ_{xy}=3/2 or 7/2.

Nonlocal supercurrent of quartets in a three-terminal Josephson junction.

A novel nonlocal supercurrent, carried by quartets, each consisting of four electrons, is expected to appear in a voltage-biased three-terminal Josephson junction. This supercurrent results from a nonlocal Andreev bound state (ABS), formed among three superconducting terminals. While in a two-terminal Josephson junction the usual ABS, and thus the dc Josephson current, exists only in equilibrium, the ABS, which gives rise to the quartet supercurrent, persists in the nonlinear regime.

Observation of half-integer thermal Hall conductance.

Topological states of matter are characterized by topological invariants, which are physical quantities whose values are quantized and do not depend on the details of the system (such as its shape, size and impurities). Of these quantities, the easiest to probe is the electrical Hall conductance, and fractional values (in units of e/h, where e is the electronic charge and h is the Planck constant) of this quantity attest to topologically ordered states, which carry quasiparticles with fractional charge and anyonic statistics. Another topological invariant is the thermal Hall conductance, which is harder to measure.

Robust integer and fractional helical modes in the quantum Hall effect.

Electronic systems harboring one-dimensional helical modes, where spin and momentum are locked, have lately become an important field of its own. When coupled to a conventional superconductor, such systems are expected to manifest topological superconductivity; a unique phase hosting exotic Majorana zero modes. Even more interesting are fractional helical modes, yet to be observed, which open the route for realizing generalized parafermions.

Transmission of heat modes across a potential barrier.

Controlling the transmission of electrical current using a quantum point contact constriction paved a way to a large variety of experiments in mesoscopic physics. The increasing interest in heat transfer in such systems fosters questions about possible manipulations of quantum heat modes that do not carry net charge (neutral modes). Here we study the transmission of upstream neutral modes through a quantum point contact in fractional hole-conjugate quantum Hall states.

Observed quantization of anyonic heat flow.

The quantum of thermal conductance of ballistic (collisionless) one-dimensional channels is a unique fundamental constant. Although the quantization of the electrical conductance of one-dimensional ballistic conductors has long been experimentally established, demonstrating the quantization of thermal conductance has been challenging as it necessitated an accurate measurement of very small temperature increase. It has been accomplished for weakly interacting systems of phonons, photons and electronic Fermi liquids; however, it should theoretically also hold in strongly interacting systems, such as those in which the fractional quantum Hall effect is observed.

Charge of a quasiparticle in a superconductor.

Nonlinear charge transport in superconductor-insulator-superconductor (SIS) Josephson junctions has a unique signature in the shuttled charge quantum between the two superconductors. In the zero-bias limit Cooper pairs, each with twice the electron charge, carry the Josephson current. An applied bias VSD leads to multiple Andreev reflections (MAR), which in the limit of weak tunneling probability should lead to integer multiples of the electron charge ne traversing the junction, with n integer larger than 2Δ/eVSD and Δ the superconducting order parameter.

Robust electron pairing in the integer quantum hall effect regime.

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.

Nonequilibrated counterpropagating edge modes in the fractional quantum Hall regime.

It is well established that density reconstruction at the edge of a two-dimensional electron gas takes place for hole-conjugate states in the fractional quantum Hall effect (such as v=2/3, 3/5, etc.). Such reconstruction leads, after equilibration between counterpropagating edge channels, to a downstream chiral current edge mode accompanied by upstream chiral neutral modes (carrying energy without net charge).

An electronic quantum eraser.

The quantum eraser is a device that illustrates the quantum principle of complementarity and shows how a dephased system can regain its lost quantum behavior by erasing the "which-path" information already obtained about it. Thus far, quantum erasers were constructed predominantly in optical systems. Here, we present a realization of a quantum eraser in a mesoscopic electronic device.

Proliferation of neutral modes in fractional quantum Hall states.

The fractional quantum Hall effect is a canonical example of topological phases. While electric currents flow downstream in edge modes, neutral edge modes, observed only in hole-conjugate states and in ν=5/2, flow upstream. It is believed that the latter transport results from multiple counter-propagating channels-mixed by disorder that is accompanied by Coulomb interaction.