Long-range nontopological edge currents in charge-neutral graphene.

Van der Waals heterostructures display numerous unique electronic properties. Nonlocal measurements, wherein a voltage is measured at contacts placed far away from the expected classical flow of charge carriers, have been widely used in the search for novel transport mechanisms, including dissipationless spin and valley transport1-9, topological charge-neutral currents10-12, hydrodynamic flows13 and helical edge modes14-16. Monolayer1-5,10,15-19, bilayer9,11,14,20 and few-layer21 graphene, transition-metal dichalcogenides6,7 and moiré superlattices8,10,12 have been found to display pronounced nonlocal effects. However, the origin of these effects is hotly debated3,11,17,22-24. Graphene, in particular, exhibits giant nonlocality at charge neutrality1,15-19, a striking behaviour that has attracted competing explanations. Using a superconducting quantum interference device on a tip (SQUID-on-tip) for nanoscale thermal and scanning gate imaging25, here we demonstrate that the commonly occurring charge accumulation at graphene edges23,26-31 leads to giant nonlocality, producing narrow conductive channels that support long-range currents. Unexpectedly, although the edge conductance has little effect on the current flow in zero magnetic field, it leads to field-induced decoupling between edge and bulk transport at moderate fields. The resulting giant nonlocality at charge neutrality and away from it produces exotic flow patterns that are sensitive to edge disorder, in which charges can flow against the global electric field. The observed one-dimensional edge transport is generic and nontopological and is expected to support nonlocal transport in many electronic systems, offering insight into the numerous controversies and linking them to long-range guided electronic states at system edges.

Mapping the twist-angle disorder and Landau levels in magic-angle graphene.

The recently discovered flat electronic bands and strongly correlated and superconducting phases in magic-angle twisted bilayer graphene (MATBG)1,2 crucially depend on the interlayer twist angle, θ. Although control of the global θ with a precision of about 0.1 degrees has been demonstrated1-7, little information is available on the distribution of the local twist angles. Here we use a nanoscale on-tip scanning superconducting quantum interference device (SQUID-on-tip)8 to obtain tomographic images of the Landau levels in the quantum Hall state9 and to map the local θ variations in hexagonal boron nitride (hBN)-encapsulated MATBG devices with relative precision better than 0.002 degrees and a spatial resolution of a few moiré periods. We find a correlation between the degree of θ disorder and the quality of the MATBG transport characteristics and show that even state-of-the-art devices-which exhibit correlated states, Landau fans and superconductivity-display considerable local variation in θ of up to 0.1 degrees, exhibiting substantial gradients and networks of jumps, and may contain areas with no local MATBG behaviour. We observe that the correlated states in MATBG are particularly fragile with respect to the twist-angle disorder. We also show that the gradients of θ generate large gate-tunable in-plane electric fields, unscreened even in the metallic regions, which profoundly alter the quantum Hall state by forming edge channels in the bulk of the sample and may affect the phase diagram of the correlated and superconducting states. We thus establish the importance of θ disorder as an unconventional type of disorder enabling the use of twist-angle gradients for bandstructure engineering, for realization of correlated phenomena and for gate-tunable built-in planar electric fields for device applications.

Publisher Correction: Imaging work and dissipation in the quantum Hall state in graphene.

An Amendment to this paper has been published and can be accessed via a link at the top of the paper.

Imaging work and dissipation in the quantum Hall state in graphene.

Topology is a powerful recent concept asserting that quantum states could be globally protected against local perturbations1,2. Dissipationless topologically protected states are therefore of major fundamental interest as well as of practical importance in metrology and quantum information technology. Although topological protection can be robust theoretically, in realistic devices it is often susceptible to various dissipative mechanisms, which are difficult to study directly because of their microscopic origins. Here we use scanning nanothermometry3 to visualize and investigate the microscopic mechanisms that undermine dissipationless transport in the quantum Hall state in graphene. Simultaneous nanoscale thermal and scanning gate microscopy shows that the dissipation is governed by crosstalk between counterpropagating pairs of downstream and upstream channels that appear at graphene boundaries as a result of edge reconstruction. Instead of local Joule heating, however, the dissipation mechanism comprises two distinct and spatially separated processes. The work-generating process that we image directly, which involves elastic tunnelling of charge carriers between the quantum channels, determines the transport properties but does not generate local heat. By contrast, the heat and entropy generation process-which we visualize independently-occurs nonlocally upon resonant inelastic scattering from single atomic defects at graphene edges, and does not affect transport. Our findings provide an insight into the mechanisms that conceal the true topological protection, and suggest routes towards engineering more robust quantum states for device applications.

A comparative study on the structural, optical and magnetic properties of Fe3O4 and Fe3O4@SiO2 core-shell microspheres along with an assessment of their potentiality as electrochemical double layer capacitors.

Herein, we report a comprehensive and comparative study on the crystal structure, and microstructural, optical, magnetic, hyperfine and electrochemical properties of Fe3O4 microspheres (S1) of diameter ∼418 nm and Fe3O4@SiO2 core-shell microspheres (S2) of diameter ∼570 nm. Each asymmetric unit of the crystalline Fe3O4 has one cation vacancy at the octahedral [B] site. At 300 K the saturation magnetization and coercivity of ferrimagnetically ordered S1 and S2 are 63.5, 38.5 emu g(-1) and 200 and 120 Oe, respectively. We have shown that the synthesis procedure, morphology, surface properties, interparticle interaction manifesting the collective properties of the nanoparticle assembly and the average size of individual Fe3O4 nanoparticles forming the spherical ensemble play a crucial role in determining the magnetic properties of Fe3O4 and Fe3O4@SiO2 microspheres while the diameter of the microsphere does not have significant influence on magnetic properties of such a system. Further, the photoluminescence intensity of Fe3O4 microspheres gets significantly enhanced upon SiO2 coating. A cyclic voltammetric study suggests that S1 can act as a good electrical double layer capacitor (EDLC) above a scan rate of 0.04 V s(-1) while S2 exhibits excellent performance as EDLC in a scan range from 0.01 to 0.06 V s(-1). Thus, S2 is a potential candidate for fabrication of EDLCs.