Counter propagating (upstream) chiral neutral edge modes, which were predicted to be present in hole-conjugate states, were observed recently in a variety of fractional quantum Hall states (v=2/3,v=3/5,v=8/3 & v=5/2), by measuring charge noise that resulted after partitioning the neutral mode by a constriction (denoted, as N\rightarrowC). Particularly noticeable was the observation of such modes in the v=5/2 fractional state - as it sheds light on the non-abelian nature of the state's wavefunction. Yet, the nature of these unique, upstream, chargeless modes and the microscopic process in which they generate shot noise, are not understood. Here, we study the ubiquitous v=2/3 state and report of two main observations: First, the nature of the neutral modes was tested by 'colliding' two modes, emanating from two opposing sources, in a narrow constriction. The resultant charge noise was consistent with local heating of the partitioned quasiparticles. Second, partitioning of a downstream charge mode by a constriction gave birth to a dual process, namely, the appearance of an upstream neutral mode (C\rightarrowN). In other words, splitting 'hole conjugated' type quasiparticles will lead to an energy loss and decoherence, with energy carried away by neutral modes.
Observations of electron-hole asymmetry in transport through graphene devices at high magnetic field challenge prevalent models of the graphene quantum Hall effect. Here, we study this asymmetry both in conventional magnetotransport and in scanning gate microscopy maps measured in an encapsulated graphene constriction. We reveal that the presence of upstream modes and local doping in the vicinity of electrical contacts leads to a totally different picture of topological breakdown for electrons and holes, explaining the observed asymmetry.
The quantum Hall effect is the seminal example of topological protection, as charge carriers are transmitted through one-dimensional edge channels where backscattering is prohibited. Graphene has made its marks as an exceptional platform to reveal new facets of this remarkable property. However, in conventional Hall bar geometries, topological protection of graphene edge channels is found regrettably less robust than in high mobility semi-conductors. Here, we explore graphene quantum Hall regime at the local scale, using a scanning gate microscope. We reveal the detrimental influence of antido…
The structure of edge modes at the boundary of quantum Hall (QH) phases forms the basis for understanding low energy transport properties. In particular, the presence of ``upstream'' modes, moving against the direction of charge current flow, 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 on noise measurements at the edges of fractional QH (FQH) phases realized in dual graphite-gated bilayer graphene devices. A noiseless dc current is injected at one of…
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 filling factor 2/3, but its applicability goes beyond that specific case, and encompasses the recent observation of ubiquitous…
Laffont et al. [Science 363, 54-57 (2019)] report an upstream current in the nu=2/3 quantum Hall regime, which, they claim, might be due to a counter-propagating charge mode. We show that this observation can also be explained by the expected upstream neutral mode, without the need for an upstream charge mode. Our results agree with the observed data and explain why the upstream current is observed only in the unpolarized nu=2/3 regime.
Upstream neutral modes, counter propagating to charge modes and carrying energy without net charge, had been predicted to exist in some of the fractional quantum Hall states and were recently observed via noise measurements. Understanding such modes will assist in identifying the wavefunction of these states, as well as shedding light on the role of Coulomb interactions within edge modes. In this work, performed mainly in the nu=2/3 state, we placed a quantum dot a few micrometers upstream of an ohmic contact, which served as a neutral modes source. We showed the neutral modes heat the input o…
Electrons living in a two-dimensional world under a strong magnetic field - the so-called fractional quantum Hall effect (FQHE) - often manifest themselves as fractionally charged quasiparticles (anyons). Moreover, being under special conditions they are expected to be immune to the environment, thus may serve as building blocks for future quantum computers. Interference of such anyons is the very first step towards understanding their anyonic statistics. However, the complex edge-modes structure of the fractional quantum Hall states, combined with upstream neutral modes, have been suspected t…
Quantum Hall phases are gapped in the bulk but support chiral edge modes, both charged and neutral. Here we consider a circuit where the path from the source of electric current to the drain necessarily passes through a segment consisting solely of neutral modes. We find that upon biasing the source, a dc electric current is detected at the drain, provided there is backscattering between counter-propagating modes under the contacts placed in certain locations. Thus, neutral modes carry information that can be used to nonlocally reconstruct a dc charge current. Our protocol can be used to detec…
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 canoni…
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 curre…
Elevated Hall Responses as Indicators of Edge Reconstruction
Indian Institute of Science Education and Research Kolkata（印度科学教育研究所加尔各答分校）；Aix Marseille Univ, Université de Toulon, CNRS, CPT（艾克斯马赛大学、土伦大学、法国国家科学研究中心、理论物理中心）
Several topological orders have been proposed to explain the quantum Hall plateau at $ν=5/2$. The observation of an upstream neutral mode on the sample edge [Bid et al., Nature (London) 466, 585 (2010)] supports the non-Abelian anti-Pfaffian state. On the other hand, the tunneling experiments [Radu et al., Science 320, 899 (2008); Lin et al., Phys. Rev. B 85, 165321 (2012); Baer et al., arXiv:1405.0428] favor the Halperin 331 state which exhibits no upstream modes. We find a topological order, compatible with the results of both types of experiments. That order allows both finite and zero spin…
We considered the nonequlibrium spin dipoles induced around spin independent elastic scatterers by the intrinsic spin-Hall effect associated with the Rashba spin-orbit coupling. The normal to 2DEG spin polarization has been calculated in the diffusion range around the scatterer. We found that although around each impurity this polarization is finite, the corresponding macroscopic spin density, obtained via averaging of individual spin dipole distributions over impurity positions is zero in the bulk. At the same time, the spin density is finite near the boundary of 2DEG, except for a special ca…
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, m…
It is well-known that a non-vanishing Hall conductivity requires time-reversal symmetry breaking. However, in this work, we demonstrate that a Hall-like transverse current can occur in second-order response to an external electric field in a wide class of time-reversal invariant and inversion breaking materials, at both zero and twice the optical frequency. This nonlinear Hall effect has a quantum origin arising from the dipole moment of the Berry curvature in momentum space, which generates a net anomalous velocity when the system is in a current-carrying state. We show that the nonlinear Hal…
We find a breather behavior of the dipole chain, this breather excitation obey fractional statistics, it could be an experimental quantity to detect anyon. A Hall effect of magnetic monopole in a dipole chain of ultracold molecules is also presented, we show that this Hall effect can induce the flip of magnetic dipole chain.
We develop a microscopic formalism to study the fractional quantum Hall plateaus at filling factors $ν$ away from $1/2β$ $β$ an integer. The theory is in terms of quasiparticles which carry a charge $e^{\ast}$ equal to $1-2βν$ times the charge of the electron. The wave functions obtained following our approach are shown to coincide precisely with the form predicted by Jain and this holds independently of the interaction potential.\ Microscopically this rigidity originates from the fact that two different charges interacting attractively in their lowest Landau levels form a bound state with a u…
In a recent experimental paper [1] a qualitative confirmation of the existence of upstream neutral modes at $ν= 2/3$ quantum Hall edge was reported. Using the chiral Luttinger liquid theory of quantum Hall edge we develop a quantitative model of the experiment [1]. A good quantitative agreement of our theory with the experimental data reinforces the conclusion of existence of the upstream neutral mode. Our model also enables us to extract important quantitative information about non-equilibrium processes in Ohmic and tunneling contacts from the experimental data. In particular, for $ν= 2/3$, w…
The fractional quantum Hall effect (FQHE) is a canonical example of a topological phase in a correlated 2D electron gas under strong magnetic field. While electric currents propagate as chiral downstream edge modes, chargeless upstream chiral neutral edge modes were recently observed only in hole-conjugate states (states filling ν, n+1/2<ν<n+1, with n=0,1,2,...), and in the even denominator state ν=5/2. It is believed that spontaneous 'density reconstruction' near the edges of the 2D gas, leads to multiple counter propagating edge channels, being separated from each other by incompressible str…
A system of electrons in two dimensions and strong magnetic fields can be tuned to create a gapped 2D system with one dimensional channels along the edge. Interactions among these edge modes can lead to independent transport of charge and heat, even in opposite directions. Measuring the chirality and transport properties of these charge and heat modes can reveal otherwise hidden structure in the edge. Here, we heat the outer edge of such a quantum Hall system using a quantum point contact. By placing quantum dots upstream and downstream along the edge of the heater, we can measure both the che…
The incommensurate phase of a bilayer quantum Hall state is found to have a ``rippled'' dipole charge density whenever the layers are unbalanced. This tunable dipole-density-wave instability could be detected by sensitive capacitance measurements and by anisotropic transport. We demonstrate this explicitly by carrying out a Hartree-Fock calculation of the layer densities and capacitance for a double-layer quantum Hall state at a total filling factor of 1.
Quasiparticles, which obey non abelian statistics, were predicted to exist in different physical systems, but are yet to be observed directly. Possible candidate states, which are expected to support such quasiparticles, are the ν=8/3, ν=5/2 and ν=7/3 fractional quantum Hall states (in the second Landau level). The non abelian quasiparticles are expected to carry charge and a unique form of a chiral neutral edge mode. Recent measurements in the ν=5/2 state detected quasiparticle charge e/4 and an upstream (opposite to charge transport) chiral neutral mode; both agreeing with a non abelian anti…
Piezotronics is an emerging field, which exploits strain to control the transport properties in condensed matters. At present, piezotronics research majorly focuses on insulators with tunable electric dipole by strain. Metals are excluded in this type of applications due to the absence of electric dipole. The recently discovered Berry curvature dipole can exist in metals, thus introduces the possibility of the piezotronics phenomena in them. In this paper, we predict that strain can switch the Berry curvature dipole, and lead the nonlinear Hall effect in the two-dimensional (2D) 1$H$-MX$_2$ (M…
We study the quantum nonlinear planar Hall effect in bilayer graphene under a steady in-plane magnetic field. When time-reversal symmetry is broken by the magnetic field, a charge current occurs in the second-order response to an external electric field, as a result of the Berry curvature dipole in momentum space. We have shown that a nonlinear planar Hall effect originating from the anomalous velocity is deduced by an orbital effect of an in-plane magnetic field on electrons in bilayer graphene in the complete absence of spin-orbit coupling. Taking into account the symmetry analysis, we deriv…
A topological phase can often be represented by a corresponding wavefunction (exact eigenstate of a model Hamiltonian) that has a higher underlying symmetry than necessary. When the symmetry is explicitly broken in the Hamiltonian, the model wavefunction fails to account for the change due to the lack of a variational parameter. Here we exemplify the case by an integer quantum Hall system with anisotropic interaction. We demonstrate the recovery of the variational parameter in a single-mode approximation, which is consistent with the recently proposed geometric consideration of the quantum Hal…
We theoretically study charge noise generated by excited neutral modes, which impinge on the quantum point contact of a quantum Hall bar with filling fraction v=2/3. The noise is computed for thermally excited neutral modes as well as for biased neutral modes with dipole-fermion excitations. Within the dipole-fermion picture, we show that the noise arising from two colliding modes can be suppressed due to Pauli-blocking and be non-universal due to random edge disorder, but becomes universal upon disorder-averaging. The ratio of noise due to two colliding neutral modes and noise due to only one…
Magnons enable transferring a magnetic moment or spin over macroscopic distance. In quantum Hall ferromagnet, it has been predicted in the early 90s that spin and charges are entangled, meaning that any change of the spin texture modifies the charge distribution. As a direct consequence of this entanglement, magnons carry an electric dipole moment. Here we report the first evidence of the existence of this electric dipole moment in a graphene quantum Hall ferromagnet using a Mach-Zehnder interferometer as a quantum sensor. By propagating towards the interferometer through an insulating bulk, t…
Light-tunable quantum metric non-linear Hall response in Berry dipole semimetals
Centre for Nanotechnology, Indian Institute of Technology Roorkee（印度理工学院鲁尔基分校纳米技术中心）；Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore（印度科学学院固态与结构化学单元）
We investigate the influence of surface states on the nonlinear Hall response of non-centrosymmetric time-reversal invariant Weyl semimetals. To do so, we perform a tomography of the Berry curvature dipole in a slab system using a minimal two-band model. We find that in the type-I phase, the nonlinear Hall response is not particularly sensitive to the presence of Fermi arcs or other trivial surface states. However, in the type-II phase, we find that these surface states contribute substantially to the Berry curvature dipole, leading to a strong thickness dependence of the nonlinear Hall respon…
The electromagnetic characteristics of double-layer quantum Hall systems are studied, with projection to the lowest Landau level taken into account and intra-Landau-level collective excitations treated in the single-mode approximation. It is pointed out that dipole-active excitations, both elementary and collective, govern the long-wavelength features of quantum Hall systems. In particular, the presence of the dipole-active interlayer out-of-phase collective excitations, inherent to double-layer systems, modifies the leading O(k) and O(k^{2}) long-wavelength characteristics (i.e., the transpor…
Various nonlinear characteristics of solid states, such as the circular photogalvanic effect of time-reversal symmetric insulators, the quantized photogalvanic effect of Weyl semimetals, and the nonlinear Hall effect of time-reversal symmetric metals, have been associated with the Berry curvature dipole (BCD). Here, we explore the question of whether the Berry curvature dipole and multipoles of time-reversal symmetric insulators can be traced in the nonlinear optical responses. We performed real-time time-dependent density functional theory calculations and examined the second harmonic generat…
Electrical and thermal conductances of a quantum Hall bar reflect the topological structure of the incompressible bulk phase. Here we show that noise of electrical current carried through the edge evidences the interplay between these two topological observables. Transport through a structured edge is modeled by a voltage-biased line junction made up of two counter-propagating modes associated with respective filling factors. Specifically, we focus on the edge of a $ν=2/3$ fractional quantum Hall state. Noise is generated at a point distinctly separated from the hot spot (where most of the Ohm…
Under broken time reversal symmetry such as in the presence of external magnetic field or internal magnetization, a transverse voltage can be established in materials perpendicular to both longitudinal current and applied magnetic field, known as classical Hall effect. However, this symmetry constraint can be relaxed in the nonlinear regime, thereby enabling nonlinear anomalous Hall current in time-reversal invariant materials - an underexplored realm with exciting new opportunities beyond classical linear Hall effect. Here, using group theory and first-principles theory, we demonstrate a rema…
The appearance of a Hall conductance necessarily requires breaking of time-reversal symmetry, either by an external magnetic field or by the internal magnetization of a material. However, as a second response, Hall dissipationless transverse currents can appear even in time-reversal symmetric conditions in non-centrosymmetric materials. Moreover, this non-linear effect has a quantum origin: it is related to the geometric properties of the electronic wavefunctions and encoded in the dipole moment of the Berry curvature. Here we review the general theory underpinning this effect and discuss vari…
Spin Hall effect (SHE) induced reversal of perpendicular magnetization has attracted significant interest, due to its potential to lead to low power memory and logic devices. However, the switching requires an assisted in-plane magnetic field, which hampers its practical applications. Here, we introduce a novel approach for external-field-free spin Hall switching of a perpendicular nanomagnet by utilizing a local dipolar field arising from an adjacent in-plane magnetic layer. Robust switching of perpendicular CoFeB nanopillars in a dipole-coupled composite stack is experimentally demonstrated …
The electronic topology is generally related to the Berry curvature, which can induce the anomalous Hall effect in time-reversal symmetry breaking systems. Intrinsic monolayer transition metal dichalcogenides possesses two nonequivalent K and K' valleys, having Berry curvatures with opposite signs, and thus vanishing anomalous Hall effect in this system. Here we report the experimental realization of asymmetrical distribution of Berry curvature in a single valley in monolayer WSe2 through applying uniaxial strain to break C3v symmetry. As a result, although the Berry curvature itself is still …
Electrons moving in a Bloch band are known to acquire an anomalous Hall velocity proportional to the Berry curvature of the band which is responsible for the intrinsic linear Hall effect in materials with broken time-reversal symmetry. Here, we demonstrate that there is also an anomalous correction to the electron acceleration which is proportional to the Berry curvature dipole and is responsible for the Nonlinear Hall effect recently discovered in materials with broken inversion symmetry. This allows us to uncover a deeper meaning of the Berry curvature dipole as a nonlinear version of the Dr…
We argue that the static non-linear Hall conductivity can always be represented as a vector in two-dimensions and as a pseudo-tensor in three-dimensions independent of its microscopic origin. In a single band model with a constant relaxation rate this vector or tensor is proportional to the Berry curvature dipole \cite{Sodemann_2015}. Here, we develop a quantum Boltzmann formalism to second order in electric fields. We find that in addition to the Berry Curvature Dipole term, there exist additional disorder mediated corrections to the non-linear Hall tensor that have the same scaling in impuri…
We demonstrate a direct approach to investigate heat transport in the fractional quantum Hall regime. At filling factor of 4/3, we inject power at quantum point contacts and detect the related heating from the activated current through a quantum dot. The experiment reveals a chargeless heat transport from a significant heating that occurs upstream of the power injection point, in the absence of a concomitant electrical current. By tuning in-situ the edge path, we show that the chargeless heat transport does not follow the reverse direction of the electrical current path along the edge. This un…
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 m…
We consider a model for an edge state of electronic systems in the quantum Hall regime with filling $ν=1$ and in the quantum spin Hall regime. In both cases the system is in contact with two reservoirs by tunneling at point contacts. Both systems are locally driven by applying an ac voltage in one of the contacts. By weakly coupling them to a third reservoir, the transport of the generated heat is studied in two different ways: i) when the third reservoir acts as a thermometer the local temperature is sensed, and ii) when the third reservoir acts as a voltage probe the time-dependent local vol…
This paper comprises a review of our recent works on fractional chiral modes that emerge due to edge reconstruction in integer and fractional quantum Hall (QH) phases. The new part added is an analysis of edge reconstruction of the $ν= 2/5$ phase. QH states are topological phases of matter featuring chiral gapless modes at the edge. These edge modes may propagate downstream or upstream, and may support either charge or charge-neutral excitations. From topological considerations, particle-like QH states are expected to support only downstream charge modes. However the interplay between the elec…
Rydberg atoms with dipole-dipole interactions provide intriguing platforms to explore exotic quantum many-body physics. Here we propose a novel scheme with laser-assisted dipole-dipole interactions to realize synthetic magnetic field for Rydberg atoms in a two-dimensional array configuration, which gives rise to the exotic bosonic topological states. In the presence of an external effective Zeeman splitting gradient, the dipole-dipole interaction between neighboring Rydberg atoms along the gradient direction is suppressed, but can be assisted when Raman lights are applied to compensate the ene…
We use the edge of the quantum Hall sample to study the possibility for counter-propagating neutral collective excitations. A novel sample design allows us to independently investigate charge and energy transport along the edge. We experimentally observe an upstream energy transfer with respect to the electron drift for the filling factors 1 and 1/3. Our analysis indicates that a neutral collective mode at the interaction-reconstructed edge is a proper candidate for the experimentally observed effect.
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 …
