The emergence of flat electronic bands and of the recently discovered strongly correlated and superconducting phases in twisted bilayer graphene crucially depends on the interlayer twist angle upon approaching the magic angle ߠ ெ ≈ 1.1°. Although advanced fabrication methods allow alignment of graphene layers with global twist angle control of about 0.1°, little information is currently available on the distribution of the local twist angles in actual magic angle twisted bilayer graphene (MATBG) transport devices. Here we map the local ߠ variations in hBN encapsulated devices with relative precision better than 0.002° and spatial resolution of a few moiré periods. Utilizing a scanning nanoSQUID-on-tip, we attain tomographic imaging of the Landau levels in the quantum Hall state in MATBG, which provides a highly sensitive probe of the charge disorder and of the local band structure determined by the local ߠ. We find a correlation between the degree of twist angle disorder and the quality of the typical MATBG transport characteristics. However, even state-of-the-art transport devices, exhibiting pronounced global MATBG features, such as multiple correlated insulator states, high-quality Landau fan diagrams, and superconductivity, display significant variations in the local ߠ with a span that can be close to 0.1°. Devices may even have substantial areas where no local MATBG behavior is detected, yet still display global MATBG characteristics in transport, highlighting the importance of percolation physics. The derived ߠ maps reveal substantial gradients and a network of jumps. We show that the twist angle gradients generate large unscreened electric fields that drastically change the quantum Hall state by forming edge states in the bulk of the sample, and may also significantly affect the phase diagram of correlated and superconducting states. The findings call for exploration of band structure engineering utilizing twist-angle gradients and gate-tunable built-in planar electric fields for novel correlated phenomena and applications.

Conversion of electric current into heat involves microscopic processes that operate on nanometer length scales and release minute amounts of power. Although central to our understanding of the electrical properties of materials, individual mediators of energy dissipation have so far eluded direct observation. Using scanning nanothermometry with submicrokelvin sensitivity, we visualized and controlled phonon emission from individual atomic-scale defects in graphene. The inferred electron-phonon "cooling power spectrum" exhibits sharp peaks when the Fermi level comes into resonance with electronic quasi-bound states at such defects. Rare in the bulk but abundant at graphene's edges, switchable atomic-scale phonon emitters provide the dominant dissipation mechanism. Our work offers insights for addressing key materials challenges in modern electronics and enables control of dissipation at the nanoscale.

Topology is a powerful recent concept asserting that quantum states could be globally protected against local perturbations [1,2]. Dissipationless topologically protected states are thus 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 fragile against various dissipative mechanisms, which are difficult to probe directly because of their microscopic origins. By utilizing scanning nanothermometry [3], we visualize and investigate microscopic mechanisms undermining the apparent topological protection in the quantum Hall state in graphene. Our 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 because 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 and which involves elastic tunneling of charge carriers between the quantum channels, determines the transport properties but does not generate local heat. The independently visualized heat and entropy generation process, in contrast, occurs nonlocally upon inelastic resonant scattering off single atomic defects at graphene edges, while not affecting the transport. Our findings offer a crucial insight into the mechanisms concealing the true topological protection and suggest venues for engineering more robust quantum states for device applications. (E.Z.) 2 In recent years, major progress has been made in identifying new topological states of matter [1,2] but the extent to which the topological protection is manifested in realistic systems and the microscopic mechanisms leading to its apparent breakdown remain poorly understood. The quantum Hall (QH) effect is a prime example of a topologically protected state exhibiting quantized dissipationless electron transport. While an extremely high degree of conductance quantization has been achieved in engineered systems in GaAs and in graphene [4], QH devices commonly exhibit small but fundamentally important deviations from the ideal quantized conductance. Various mechanisms undermining the topological protection were explored, including imperfect contacts [5], current-induced breakdown [4], absence of edge equilibration [6], and edge reconstruction [7,8]. Nonetheless, how exactly the dissipation in the QH regime occurs on a microscopic level has eluded direct identification. Here we provide nanoscale imaging of the dissipation processes in the QH state in graphene and reveal the intricate mechanisms compromising the apparent global topological protection.A superconducting quantum interference device, SQUID-on-tip (SOT) [9] acting as nanothermometer (tSOT) with µK sensitivity [3] and effective diameter of ~50 nm was scanned ~50 nm above high-mobility hBN-encapsu...

The authors find that for mechanically milled Ni0.5Zn0.5Fe2O4 (∼10 nm), the mechanical strain induced enhancement of anisotropy energy helps to retain stable magnetic order. The reduction of magnetization can be prevented by keeping the cation distribution of nanometric ferrites at its equilibrium ratio. Moreover, the sample can be used in coding, storing, and retrieving of binary bit (“0” and “1”) through magnetic field change.

The recently predicted topological magnetoelectric effect [1] and the response to an electric charge that mimics an induced mirror magnetic monopole [2] are fundamental attributes of topological states of matter with broken time reversal symmetry. Using a SQUID-on-tip [3], acting simultaneously as a tunable scanning electric charge and as ultrasensitive nanoscale magnetometer, we induce and directly image the microscopic currents generating the magnetic monopole response in a graphene quantum Hall electron system. We find a rich and complex nonlinear behavior governed by coexistence of topological and nontopological equilibrium currents that is not captured by the monopole models [2]. Furthermore, by utilizing a tuning fork that induces nanoscale vibrations of the SQUID-on-tip, we directly image the equilibrium currents of individual quantum Hall edge states for the first time. We reveal that the edge states that are commonly assumed to carry only a chiral downstream current, in fact carry a pair of counterpropagating currents [4], in which the topological downstream current in the incompressible region is always counterbalanced by heretofore unobserved nontopological upstream current flowing in the adjacent compressible region. The intricate patterns of the counterpropagating equilibrium-state orbital currents provide new insights into the microscopic origins of the topological and nontopological charge and energy flow in quantum Hall systems. * Corresponding authors SM1. Device fabricationThree graphene based van der Waals heterostructures were measured (Fig. S1). All devices consisted of an hBN/graphene/hBN stack placed on top of the 300 nm thick SiO 2 layer of a thermally oxidized doped silicon wafer, acting as a backgate. A graphitic layer was placed under part of the stack, serving as an additional backgate. The two backgates allowed to induce an interface of two different filling factors, ߥ and ߥ ோ , at the boundary of the graphitic layer (Fig. 3a). The van der Waals stacking of device A, was carried out with the viscoelastic transfer method as explained in Ref. [32]. Device B and C were created with the ELVACITE based pick-up method reported in Refs. [32,33]. In order to minimize the SOT distance to graphene, we used a relatively thin top hBN layer with a thickness of approximately 8 nm (devices A and C) and 11.5 nm (device B). The bottom hBN layer was 23 nm (device A) and 50 nm (devices B and C). The graphite backgate layer had a thickness of approximately 5 nm. The heterostructures were annealed in an Ar/H 2 forming gas atmosphere at 500°C to remove bubbles and wrinkles prior to further processing. Patterning was performed using electron beam lithography and etching as described in Ref.[34]. Contacts and leads were fabricated by thermal evaporation of a 10 nm thick Cr adhesion layer followed by a 50-70 nm Au layer. The SOT scanning studies require an exceptionally clean surface. To ensure this, extra cleaning steps were carried out. After lift-off, devices were re-annealed at 350°C. Contact mode atomic...