Proliferation of neutral modes in fractional quantum Hall states

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 disorder1-9. 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 density3. Still, the details of the localized states and their contribution to transport remain beyond the reach of most experimental techniques10-31. Here we describe an extensive study of the bulk's heat conductance. Using a novel 'multiterminal' short device (on a scale of 10 µm), we separate the longitudinal thermal conductance, [Formula: see text] (owing to the bulk's contribution), from the topological transverse value [Formula: see text] by eliminating the contribution of the edge modes24. When the magnetic field is tuned away from the conductance plateau centre, the localized states in the bulk conduct heat efficiently ([Formula: see text]), whereas the bulk remains electrically insulating. Fractional states in the first excited Landau level, such as the [Formula: see text] and [Formula: see text], conduct heat throughout the plateau with a finite [Formula: see text]. We propose a theoretical model that identifies the localized states as the cause of the finite heat conductance, agreeing qualitatively with our experimental findings.

Quasiparticle Andreev scattering in the ν = 1/3 fractional quantum Hall regime

The scattering of exotic quasiparticles may follow different rules than electrons. In the fractional quantum Hall regime, a quantum point contact (QPC) provides a source of quasiparticles with field effect selectable charges and statistics, which can be scattered on an 'analyzer' QPC to investigate these rules. Remarkably, for incident quasiparticles dissimilar to those naturally transmitted across the analyzer, electrical conduction conserves neither the nature nor the number of the quasiparticles. In contrast with standard elastic scattering, theory predicts the emergence of a mechanism akin to the Andreev reflection at a normal-superconductor interface. Here, we observe the predicted Andreev-like reflection of an e/3 quasiparticle into a - 2e/3 hole accompanied by the transmission of an e quasielectron. Combining shot noise and cross-correlation measurements, we independently determine the charge of the different particles and ascertain the coincidence of quasielectron and fractional hole. The present work advances our understanding on the unconventional behavior of fractional quasiparticles, with implications toward the generation of novel quasi-particles/holes and non-local entanglements.

Emergence of Neutral Modes in Laughlin-like Fractional Quantum Hall Phases

Chiral gapless boundary modes are characteristic of quantum Hall (QH) states. For hole-conjugate fractional QH phases counterpropagating edge modes (upstream and downstream) are expected. In the presence of electrostatic interactions and disorder these modes may renormalize into charge and upstream neutral modes. Orthodox models of Laughlin phases anticipate only a downstream charge mode. Here we show that in the latter case, in the presence of a smooth confining potential, edge reconstruction leads to the emergence of pairs of counterpropagating modes, which, by way of mode renormalization, may give rise to nontopological upstream neutral modes, possessing nontrivial statistics. This may explain the experimental observation of ubiquitous neutral modes, and the overwhelming suppression of anyonic interference in Mach-Zehnder interferometry platforms. We also point out other signatures of such edge reconstruction.

Heat Equilibration of Integer and Fractional Quantum Hall Edge Modes in Graphene

Hole-conjugate states of the fractional quantum Hall effect host counterpropagating edge channels which are thought to exchange charge and energy. These exchanges have been the subject of extensive theoretical and experimental works; in particular, it is yet unclear if the presence of integer quantum Hall edge channels stemming from fully filled Landau levels affects heat equilibration along the edge. In this Letter, we present heat transport measurements in quantum Hall states of graphene demonstrating that the integer channels can strongly equilibrate with the fractional ones, leading to markedly different regimes of quantized heat transport that depend on edge electrostatics. Our results allow for a better comprehension of the complex edge physics in the fractional quantum Hall regime.

Transport in helical Luttinger liquids in the fractional quantum Hall regime

Domain walls in fractional quantum Hall ferromagnets are gapless helical one-dimensional channels formed at the boundaries of topologically distinct quantum Hall (QH) liquids. Naïvely, these helical domain walls (hDWs) constitute two counter-propagating chiral states with opposite spins. Coupled to an s-wave superconductor, helical channels are expected to lead to topological superconductivity with high order non-Abelian excitations^1–3. Here we investigate transport properties of hDWs in the ν = 2/3 fractional QH regime. Experimentally we found that current carried by hDWs is substantially smaller than the prediction of the naïve model. Luttinger liquid theory of the system reveals redistribution of currents between quasiparticle charge, spin and neutral modes, and predicts the reduction of the hDW current. Inclusion of spin-non-conserving tunneling processes reconciles theory with experiment. The theory confirms emergence of spin modes required for the formation of fractional topological superconductivity.

Previous work has shown that helical domain walls can form between states of different spin-polarization during a ferromagnetic spin transition in the fractional quantum Hall regime. Here, the authors study the transport through a single helical domain wall and find strong deviations from a simplified theory of weakly interacting edge channels.

Anomalous Hydrodynamics in a One-Dimensional Electronic Fluid

We construct multimode viscous hydrodynamics for one-dimensional spinless electrons. Depending on the scale, the fluid has six (shortest lengths), four (intermediate, exponentially broad regime), or three (asymptotically long scales) hydrodynamic modes. Interaction between hydrodynamic modes leads to anomalous scaling of physical observables and waves propagating in the fluid. In the four-mode regime, all modes are ballistic and acquire Kardar-Parisi-Zhang (KPZ)-like broadening with asymmetric power-law tails. "Heads" and "tails" of the waves contribute equally to thermal conductivity, leading to ω^{-1/3} scaling of its real part. In the three-mode regime, the system is in the universality class of a classical viscous fluid [O. Narayan and S. Ramaswamy, Anomalous Heat Conduction in One-Dimensional Momentum-Conserving Systems, Phys. Rev. Lett. 89, 200601 (2002).PRLTAO0031-900710.1103/PhysRevLett.89.200601, H. Spohn, Nonlinear fluctuating hydrodynamics for anharmonic chains, J. Stat. Phys. 154, 1191 (2014).JSTPBS0022-471510.1007/s10955-014-0933-y]. Self-interaction of the sound modes results in a KPZ-like shape, while the interaction with the heat mode results in asymmetric tails. The heat mode is governed by Levy flight distribution, whose power-law tails give rise to ω^{-1/3} scaling of heat conductivity.

Fractional charge and fractional statistics in the quantum Hall effects

Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be observed. In addition to theoretical foundations, we review the present status of the experiments in the area. We also discuss the notions of non-Abelian statistics and attempts to find experimental evidence for the existence of non-Abelian quasiparticles in certain quantum Hall systems.

Magnetic-Field-Dependent Equilibration of Fractional Quantum Hall Edge Modes

Fractional conductance is measured by partitioning a ν=1 edge state using gate-tunable fractional quantum Hall (FQH) liquids of filling 1/3 or 2/3 for current injection and detection. We observe two sets of FQH plateaus 1/9, 2/9, 4/9 and 1/6, 1/3, 2/3 at low and high magnetic field ends of the ν=1 plateau, respectively. The findings are explained by magnetic field dependent equilibration of three FQH edge modes with conductance e^{2}/3h arising from edge reconstruction. The results reveal a remarkable enhancement of the equilibration lengths of the FQH edge modes with increasing magnetic field.

Fractional statistics in anyon collisions

Two-dimensional systems can host exotic particles called anyons whose quantum statistics are neither bosonic nor fermionic. For example, the elementary excitations of the fractional quantum Hall effect at filling factor ν = 1/m (where m is an odd integer) have been predicted to obey Abelian fractional statistics, with a phase ϕ associated with the exchange of two particles equal to π/m However, despite numerous experimental attempts, clear signatures of fractional statistics have remained elusive. We experimentally demonstrate Abelian fractional statistics at filling factor ν = ⅓ by measuring the current correlations resulting from the collision between anyons at a beamsplitter. By analyzing their dependence on the anyon current impinging on the splitter and comparing with recent theoretical models, we extract ϕ = π/3, in agreement with predictions.

Electronic heat flow and thermal shot noise in quantum circuits

When assembling individual quantum components into a mesoscopic circuit, the interplay between Coulomb interaction and charge granularity breaks down the classical laws of electrical impedance composition. Here we explore experimentally the thermal consequences, and observe an additional quantum mechanism of electronic heat transport. The investigated, broadly tunable test-bed circuit is composed of a micron-scale metallic node connected to one electronic channel and a resistance. Heating up the node with Joule dissipation, we separately determine, from complementary noise measurements, both its temperature and the thermal shot noise induced by the temperature difference across the channel. The thermal shot noise predictions are thereby directly validated, and the electronic heat flow is revealed. The latter exhibits a contribution from the channel involving the electrons' partitioning together with the Coulomb interaction. Expanding heat current predictions to include the thermal shot noise, we find a quantitative agreement with experiments.

Universal quantized thermal conductance in graphene

The universal quantization of thermal conductance provides information on a state's topological order. Recent measurements revealed that the observed value of thermal conductance of the 5 2 state is inconsistent with either Pfaffian or anti-Pfaffian model, motivating several theoretical articles. Analysis has been made complicated by the presence of counter-propagating edge channels arising from edge reconstruction, an inevitable consequence of separating the dopant layer from the GaAs quantum well and the resulting soft confining potential. Here, we measured thermal conductance in graphene with atomically sharp confining potential by using sensitive noise thermometry on hexagonal boron-nitride encapsulated graphene devices, gated by either SiO₂/Si or graphite back gate. We find the quantization of thermal conductance within 5% accuracy for ν = 1 ; 4 3 ; 2 and 6 plateaus, emphasizing the universality of flow of information. These graphene quantum Hall thermal transport measurements will allow new insight into exotic systems like even-denominator quantum Hall fractions in graphene.

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. We have confirmed the presence of upstream neutral modes measuring upstream noise emanating from the QPC. The lack of interference throughout the lowest Landau level was correlated with a proliferation of neutral modes.

Thermal Transport in One-Dimensional Electronic Fluids

We study thermal conductivity for one-dimensional electronic fluids. The many-body Hilbert space is partitioned into bosonic and fermionic sectors that carry the thermal current in parallel. For times shorter than the bosonic umklapp time, the momenta of Bose and Fermi components are separately conserved, giving rise to the ballistic heat propagation and imaginary heat conductivity proportional to T/iω. The real part of thermal conductivity is controlled by decay processes of fermionic and bosonic excitations, leading to several regimes in frequency dependence. At lowest frequencies or longest length scales, the thermal transport is dominated by Lévy flights of low-momentum bosons that lead to a fractional scaling, ω^{-1/3} and L^{1/3}, of heat conductivity with the frequency ω and system size L, respectively.

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. Here, we present an approach to synthetize a v = 2/3 edge mode from its basic counter-propagating charged constituents, allowing a controlled equilibration between the two counter-propagating charge modes. This platform is based on a carefully designed double-quantum-well, which hosts two populated electronic sub-bands (lower and upper), with corresponding filling factors, v_l and v_u. By separating the 2D plane to two gated intersecting halves, each with different fillings, counter-propagating chiral modes can be formed along the intersection line. Equilibration between these modes can be controlled with the top gates’ voltage and the magnetic field.

The boundaries of fractional quantum Hall states can host multiple, interacting one-dimensional edge modes, which test our understanding of strongly interacting systems. Here the authors observe the edge-mode equilibration transition that was predicted for the ν=2/3 fractional quantum Hall state.

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. However, so far, charge currents were observed to flow exclusively downstream in the quantum Hall regime. Studying the canonical spin-polarized and spin-unpolarized v = 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.

Fractional Quantum Hall Effect at ν=2+6/13: The Parton Paradigm for the Second Landau Level

The unexpected appearance of a fractional quantum Hall effect (FQHE) plateau at ν=2+6/13 [A. Kumar et al., Phys. Rev. Lett. 105, 246808 (2010)PRLTAO0031-900710.1103/PhysRevLett.105.246808] offers a clue into the physical mechanism of the FQHE in the second Landau level (SLL). Here we propose a "3[over ¯]2[over ¯]111" parton wave function, which is topologically distinct from the 6/13 state in the lowest Landau level. We demonstrate the 3[over ¯]2[over ¯]111 state to be a good candidate for the ν=2+6/13 FQHE, and make predictions for experimentally measurable properties that can reveal the nature of this state. Furthermore, we propose that the "n[over ¯]2[over ¯]111" family of parton states naturally describes many observed SLL FQHE plateaus.

Oxygen-dependent generation of a graded polydopamine coating on nanofibrous materials for controlling stem cell functions

A nanofiber with gradient in polydopamine coating was generated by controlling oxidative polymerization of dopamine for tuning stem cell responses.

Suppression of Interference in Quantum Hall Mach-Zehnder Geometry by Upstream Neutral Modes

Mach-Zehnder interferometry has been proposed as a probe for detecting the statistics of anyonic quasiparticles in fractional quantum Hall (FQH) states. Here, we focus on interferometers made of multimode edge states with upstream modes. We find that the interference visibility is suppressed due to downstream-upstream mode entanglement; the latter serves as a "which path" detector to the downstream interfering trajectories. Our analysis tackles a concrete realization of a filling factor of ν=2/3, but its applicability goes beyond that specific case, and encompasses the recent observation of the ubiquitous emergence of upstream neutral modes in FQH states. The latter, according to our analysis, goes hand in hand with the failure to observe Mach-Zehnder anyonic interference in fractional states. We point out how charge-neutral mode disentanglement will resuscitate the interference signal.

Stabilization of the Particle-Hole Pfaffian Order by Landau-Level Mixing and Impurities That Break Particle-Hole Symmetry

Numerical results suggest that the quantum Hall effect at ν=5/2 is described by the Pfaffian or anti-Pfaffian state in the absence of disorder and Landau-level mixing. Those states are incompatible with the observed transport properties of GaAs heterostructures, where disorder and Landau-level mixing are strong. We show that the recent proposal of a particle-hole (PH)-Pfaffian topological order by Son is consistent with all experiments. The absence of particle-hole symmetry at ν=5/2 is not an obstacle to the existence of the PH-Pfaffian order since the order is robust to symmetry breaking.

Coulomb blockade with neutral modes

We study transport through a quantum dot in the fractional quantum Hall regime with filling factors ν=2/3 and ν=5/2, weakly coupled to the leads. We account for both injection of electrons to or from the leads, and quasiparticle rearrangement processes between the edge and the bulk of the quantum dot. The presence of neutral modes introduces topological constraints that modify qualitatively the features of the Coulomb blockade (CB). The periodicity of CB peak spacings doubles and the ratio of spacing between adjacent peaks approaches (in the low temperature and large dot limit) a universal value: 2∶1 for ν=2/3 and 3∶1 for ν=5/2. The corresponding CB diamonds alternate their width in the direction of the bias voltage and allow for the determination of the neutral mode velocity, and of the topological numbers associated with it.

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). Short equilibration length prevented thus far observation of the counterpropagating current channels-the hallmark of density reconstruction. Here, we provide evidence for such nonequilibrated counterpropagating current channels, in short regions (l=4  μm and l=0.4  μm) of fractional filling v=2/3 and, unexpectedly, v=1/3, sandwiched between two regions of integer filling v=1. Rather than a two-terminal fractional conductance, the conductance exhibited a significant ascension towards unity quantum conductance (GQ=e(2)/h) at or near the fractional plateaus. We attribute this conductance rise to the presence of a nonequilibrated channel in the fractional short regions.

Recent experimental progress of fractional quantum Hall effect: 5/2 filling state and graphene

The phenomenon of fractional quantum Hall effect (FQHE) was first experimentally observed 33 years ago. FQHE involves strong Coulomb interactions and correlations among the electrons, which leads to quasiparticles with fractional elementary charge. Three decades later, the field of FQHE is still active with new discoveries and new technical developments. A significant portion of attention in FQHE has been dedicated to filling factor 5/2 state, for its unusual even denominator and possible application in topological quantum computation. Traditionally, FQHE has been observed in high-mobility GaAs heterostructure, but new materials such as graphene also open up a new area for FQHE. This review focuses on recent progress of FQHE at 5/2 state and FQHE in graphene.