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Studies of energy flow in quantum systems complement the information provided by common conductance measurements. The quantum limit of heat flow in one dimensional (1D) 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. Nevertheless, open questions about energy relaxation along the propagation length in 1D modes remain. Here, we introduce a novel experimental setup that measures the energy relaxation in chiral 1D modes of the quantum Hall effect (QHE). Edge modes, emanating from a heated reservoir, are partitioned by a quantum point contact (QPC) located at their path. The resulting noise allows a determination of the 'effective temperature' at the location of the QPC. We found energy relaxation in all the tested QHE states, being integers or fractional. However, the relaxation was found to be mild in particle-like states, and prominent in hole-conjugate states.

The quantum Hall effect, observed in a two-dimensional 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. However, so far, charge currents were observed to flow exclusively downstream in the quantum Hall regime. Studying the canonical spin-polarized and spin-unpolarized $\nu=2/3$ hole-like states in GaAs-AlGaAs heterostructures, we observed a significant upstream charge current at short propagation distances in the spin unpolarized state

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. Employing two different measurement techniques, we were able to render the relative spatial distribution of these chargeless modes with their charged counter-parts. In these states, which were found to harbor more than one downstream charge mode, the upstream neutral modes are found to flow with the inner charge mode - as theoretically predicted. These results unveil a universal upstream heat current structure and open the path for more complex engineering of heat flows and cooling mechanisms in quantum nano-electronic devices.

The quantum of heat conductance of ballistic one-dimensional (1D) channels, being gQ=k0T with k0=pi^2*2kB^2/3h (T - temperature, kB - Boltzmann's constant, h - Planck's constant), is an important fundamental constant. While the quantization of the electrical conductance of 1D ballistic conductors has long been experimentally established, a demonstration of the quantization of thermal conductance proved to be much harder. It has already been accomplished for weakly interacting systems of phonons, photons, and electronic Fermi-liquids. Theoretically, however, the quantization must also hold in strongly interacting systems, such as the Fractional Quantum Hall effect (FQHE), where electrons fractionalize into anyons and chargeless quasiparticles such as neutral Majorana fermions. Since the bulk in the FQHE is incompressible, it is not expected to contribute significantly to the heat conductance, which is determined by chiral 1D edge modes. The thermal conductance reflects topological properties of the FQH electronic systems to which the electrical conductance gives no access. Here, we present results of extensive measurements of the heat conductance in 'particle-like' (Laughlin's) and 'hole-like' fractional states. We verify the universal value of the quantum of thermal conductance of the charged fractional modes as well as for chargeless neutral modes. We also prove the validity of the theoretical predictions for the more complex (and less studied) 'hole-like' states. Heat transport measurements open a door to ample information, not easily accessible by conductance measurements.

The recent, unexpected, findings of upstream neutral modes in particle-like fractional quantum Hall states, led to a realization that the nature of the neutral modes is far from being understood. Moreover, the observation of spatially separated of (at least) two downstream charge modes in hole-conjugate states (see Part One - Conductance), still faces unresolved contradictions between conductance and noise measurements. In this work we show how current fluctuations measured in various configurations shed light on the interplay between neutral and charge modes. We demonstrate that once one of the charge modes is taken out of equilibrium, counter-propagating neutral modes born in the equilibration process affect the upstream charge modes, giving rise to a novel mechanism for shot noise with quantized Fano factors. We present a theoretical model that accounts for most of the experimental observations., Comment: The results presented here were merged into another submission. see arXiv:1603.06908

Questions on the nature of edge reconstruction and "where does the current flow" in the quantum Hall effect (QHE) have been debated for years. Moreover, the recent observation of proliferation of "upstream" neutral modes in the fractional QHE raised doubts about the present models of edge channels. In this article we focus on hole-conjugate states, nu=2/3 and nu=3/5, and present a new picture of their edge reconstruction. For example, while the present model for nu=2/3 consists of a single downstream charge channel with conductance 2/3 e^2/h and an upstream neutral mode, we show that the current is carried by two separate downstream edge channels, each with conductance 1/3 e^2/h, accompanied by upstream neutral mode(s). We find that if the two downstream channels are not equilibrated, inter-mode equilibration (via particle exchange) takes place over a distance of microns, with the two channels effectively behaving as a single channel. Moreover, the inter-channel equilibration is accompanied by an excitation of upstream neutral modes. In turn, the counter-propagating neutral modes, moving in close proximity to the charge modes, fragment into propagating charges, inducing thus downstream current fluctuations with zero net current - a novel mechanism for non-equilibrium noise. This unexpected edge reconstruction underlines the need for better understanding of edge reconstruction and energy transport in all fractional QHE states.

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.These studies found the ubiquitous electronic Fabry-Perot interferometer to be Coulomb dominated, thus masking coherent Aharonov-Bohm interference. Typically, the main signature of the Coulomb dominated regime is the lack of interference of the outer most edge channel as the magnetic field is varied. This seemingly surprising behavior is explained by the shrinkage of the interference area with increasing magnetic field, thus keeping the number of electrons and the enclosed flux constant. The model further stipulates, but with no experimental evidence thus far, that once the area shrinks by a size corresponding to an entire flux-quantum, it abruptly inflates to its original size leading to an unobservable 2{\pi} phase jump. Here we report on the observation of such area breathing by performing a partial screening of the Coulomb interactions. The novelty is that the variation of the phase induced by the external knobs is not fully cancelled by the area response. We infer the area variations (with a resolution on the order of ~50 nm$^{2}$) from conductance measurements. The latter are sensitive to the continuous phase variations, and reveal abrupt phase-jumps (smaller than 2{\pi}). Based on our results, we propose a new experimental tool for probing anyonic statistics.

Electron pairing is a rare phenomenon appearing only in a few unique physical systems; e.g., superconductors and Kondo-correlated quantum dots. Here, we report on an unexpected, but robust, electron "pairing" in the integer quantum Hall effect (IQHE) regime. The pairing takes place within an interfering edge channel circulating in an electronic Fabry-Perot interferometer at a wide range of bulk filling factors, $2<{\nu} _B<5$. The main observations are: (a) High visibility Aharonov-Bohm conductance oscillations with magnetic flux periodicity ${\Delta}{\phi}={\varphi}_0/2=h/2e$ (instead of the ubiquitous $h/e$), with $e$ the electron charge and $h$ the Planck constant; (b) An interfering quasiparticle charge $e ^* {\sim} 2e$ - revealed by quantum shot noise measurements; and (c) Full dephasing of the $h/2e$ periodicity by induced dephasing of the adjacent edge channel (while keeping the interfering edge channel intact) : a clear realization of inter-channel entanglement. While this pairing phenomenon clearly results from inter-channel interaction, the exact mechanism that leads to e-e attraction within a single edge channel is not clear.