Topological Classification of Shot Noise on Fractional Quantum Hall Edges

Landscapes of an Out-of-Equilibrium Anyonic Sea

The low-energy dynamics of two-dimensional topological matter hinges on its one-dimensional edge modes. Tunneling between fractional quantum Hall edge modes facilitates the study of anyonic statistics: it induces time-domain braiding that dominates signals from diluted anyon beams. We develop a framework for characterizing one-dimensional out-of-equilibrium anyonic states and define their effective potential and temperature, both arising from anyonic braiding, as well as the landscape of their excitations. Unlike fermions, the effective anyon potential depends on the type of the tunneling quasiparticles; nonequilibrium anyonic states are underlain by power-law energy distributions. This allows "hot" anyons to tunnel above the chemical potential of the source, which we capture by a measurable universal witness function. Our analysis raises the prospect of generalizing the kinetic approach to compressible anyonic matter in higher dimensions.

Fingerprints of Anti-Pfaffian Topological Order in Quantum Point Contact Transport

Despite recent experimental developments, the topological order of the fractional quantum Hall state at filling ν=5/2 remains an outstanding question. We study conductance and shot noise in a quantum point contact device in the charge-equilibrated regime and show that, among Pfaffian, particle-hole Praffian, and anti-Pfaffian (aPf) candidate states, the hole-conjugate aPf state is unique in that it can produce a conductance plateau at G=(7/3)e^{2}/h by two fundamentally distinct mechanisms. We demonstrate that these mechanisms can be distinguished by shot noise measurements on the plateaus. We also determine distinct features of the conductance of the aPf state in the coherent regime. Our results can be used to experimentally single out the aPf order.

Electrical noise spectroscopy of magnons in a quantum Hall ferromagnet

Collective spin-wave excitations, magnons, are promising quasi-particles for next-generation spintronics devices, including platforms for information transfer. In a quantum Hall ferromagnets, detection of these charge-neutral excitations relies on the conversion of magnons into electrical signals in the form of excess electrons and holes, but if the excess electron and holes are equal, detecting an electrical signal is challenging. In this work, we overcome this shortcoming by measuring the electrical noise generated by magnons. We use the symmetry-broken quantum Hall ferromagnet of the zeroth Landau level in graphene to launch magnons. Absorption of these magnons creates excess noise above the Zeeman energy and remains finite even when the average electrical signal is zero. Moreover, we formulate a theoretical model in which the noise is produced by equilibration between edge channels and propagating magnons. Our model also allows us to pinpoint the regime of ballistic magnon transport in our device.

Full Classification of Transport on an Equilibrated 5/2 Edge via Shot Noise

The nature of the bulk topological order of the 5/2 non-Abelian fractional quantum Hall state and the steady state of its edge are long-studied questions. The most promising non-Abelian model bulk states are the Pfaffian (Pf), anti-Pffafian (APf), and particle-hole symmetric Pfaffian (PHPf). Here, we propose to employ a set of dc current-current correlations (electrical shot noise) in order to distinguish among the Pf, APf, and PHPf candidate states, as well as to determine their edge thermal equilibration regimes: full vs partial. Using other tools, measurements of GaAs platforms have already indicated consistency with the PHPf state. Our protocol, realizable with available experimental tools, is based on fully electrical measurements.

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.

Absent thermal equilibration on fractional quantum Hall edges over macroscopic scale

Two-dimensional topological insulators, and in particular quantum Hall states, are characterized by an insulating bulk and a conducting edge. Fractional states may host both downstream (dictated by the magnetic field) and upstream propagating edge modes, which leads to complex transport behavior. Here, we combine two measurement techniques, local noise thermometry and thermal conductance, to study thermal properties of states with counter-propagating edge modes. We find that, while charge equilibration between counter-propagating edge modes is very fast, the equilibration of heat is extremely inefficient, leading to an almost ballistic heat transport over macroscopic distances. Moreover, we observe an emergent quantization of the heat conductance associated with a strong interaction fixed point of the edge modes. Such understanding of the thermal equilibration on edges with counter-propagating modes is a natural route towards extracting the topological order of the exotic 5/2 state.

The transport behaviour of counter-propagating edge modes in the hole-conjugate fractional quantum Hall state is not fully understood. Here, by combining local noise thermometry and thermal conductance measurements, the authors show the absence of thermal equilibration on the edge at macroscopic distances.

Observation of ballistic upstream modes at fractional quantum Hall edges of graphene

The presence of "upstream" modes, moving against the direction of charge current flow in the fractional quantum Hall (FQH) phases, is critical for the emergence of renormalized modes with exotic quantum statistics. Detection of excess noise at the edge is a smoking gun for the presence of upstream modes. Here, we report noise measurements at the edges of FQH states realized in dual graphite-gated bilayer graphene devices. A noiseless dc current is injected at one of the edge contacts, and the noise generated at contacts at length, L = 4 μm and 10 μm away along the upstream direction is studied. For integer and particle-like FQH states, no detectable noise is measured. By contrast, for "hole-conjugate" FQH states, we detect a strong noise proportional to the injected current, unambiguously proving the existence of upstream modes. The noise magnitude remains independent of length, which matches our theoretical analysis demonstrating the ballistic nature of upstream energy transport, quite distinct from the diffusive propagation reported earlier in GaAs-based systems.

Distinguishing between non-abelian topological orders in a Quantum Hall system

[Figure: see text].

Fractionalized conductivity and emergent self-duality near topological phase transitions

The experimental discovery of the fractional Hall conductivity in two-dimensional electron gases revealed new types of quantum particles, called anyons, which are beyond bosons and fermions as they possess fractionalized exchange statistics. These anyons are usually studied deep inside an insulating topological phase. It is natural to ask whether such fractionalization can be detected more broadly, say near a phase transition from a conventional to a topological phase. To answer this question, we study a strongly correlated quantum phase transition between a topological state, called a [Formula: see text] quantum spin liquid, and a conventional superfluid using large-scale quantum Monte Carlo simulations. Our results show that the universal conductivity at the quantum critical point becomes a simple fraction of its value at the conventional insulator-to-superfluid transition. Moreover, a dynamically self-dual optical conductivity emerges at low temperatures above the transition point, indicating the presence of the elusive vison particles. Our study opens the door for the experimental detection of anyons in a broader regime, and has ramifications in the study of quantum materials, programmable quantum simulators, and ultra-cold atomic gases. In the latter case, we discuss the feasibility of measurements in optical lattices using current techniques.

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.

Vanishing Thermal Equilibration for Hole-Conjugate Fractional Quantum Hall States in Graphene

Transport through edge channels is responsible for conduction in quantum Hall (QH) phases. Robust quantized values of charge and thermal conductances dictated by bulk topology appear when equilibration processes become dominant. We report on measurements of electrical and thermal conductances of integer and fractional QH phases, realized in hexagonal boron nitride encapsulated graphite-gated bilayer graphene devices for both electron and hole doped sides with different valley and orbital symmetries. Remarkably, for complex edges at filling factors ν=5/3 and 8/3, closely related to the paradigmatic hole-conjugate ν=2/3 phase, we find quantized thermal conductance whose values (3κ_{0}T and 4κ_{0}T, respectively where κ_{0}T is the thermal conductance quantum) are markedly inconsistent with the values dictated by topology (1κ_{0}T and 2κ_{0}T, respectively). The measured thermal conductance values remain insensitive to different symmetries, suggesting its universal nature. Our findings are supported by a theoretical analysis, which indicates that, whereas electrical equilibration at the edge is established over a finite length scale, the thermal equilibration length diverges for strong electrostatic interaction. Our results elucidate the subtle nature of crossover from coherent, mesoscopic to topology-dominated transport.

Quantized charge fractionalization at quantum Hall Y junctions in the disorder dominated regime

Fractionalization is a phenomenon where an elementary excitation partitions into several pieces. This picture explains non-trivial transport through a junction of one-dimensional edge channels defined by topologically distinct quantum Hall states, for example, a hole-conjugate state at Landau-level filling factor ν = 2/3. Here we employ a time-resolved scheme to identify an elementary fractionalization process; injection of charge q from a non-interaction region into an interacting and scattering region of one-dimensional channels results in the formation of a collective excitation with charge (1-r)q by reflecting fractionalized charge rq. The fractionalization factors, r = 0.34 ± 0.03 for ν = 2/3 and r = 0.49 ± 0.03 for ν = 2, are consistent with the quantized values of 1/3 and 1/2, respectively, which are expected in the disorder dominated regime. The scheme can be used for generating and transporting fractionalized charges with a well-defined time course along a well-defined path.

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. In such exotic states, thermal-energy relaxation along the edge is expected, and can shed light on their topological nature. Here, we introduce a novel experimental setup that enables a direct observation of thermal-energy relaxation in chiral 1D edge modes in the quantum Hall effect. Edge modes, emanating from a heated reservoir, are partitioned by a quantum point contact (QPC) constriction, which is located at some distance along their path. The resulting low frequency noise, measured downstream, allows determination of the "effective temperature" of the edge mode at the location of the QPC. An expected, prominent energy relaxation was found in hole-conjugate states. However, relaxation was also observed in particlelike states, where heat is expected to be conserved. We developed a model, consisting of distance-dependent energy loss, which agrees with the observations; however, we cannot exclude energy redistribution mechanisms, which are not accompanied with energy loss.

Noise on the non-Abelian ν=5/2 Fractional Quantum Hall Edge

The recent measurement of a half-integer thermal conductance for the ν=5/2 fractional quantum Hall state has confirmed its non-Abelian nature, making the question of the underlying topological order highly intriguing. We analyze the shot noise at the edge of the three most prominent non-Abelian candidate states. We show that the noise scaling with respect to the edge length can, in combination with the thermal conductance, be used to experimentally distinguish between the Pfaffian, anti-Pfaffian, and particle-hole-Pfaffian edge structures.