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.

Energy dissipation is a fundamental process governing the dynamics of physical, chemical, and biological systems. It is also one of the main characteristics distinguishing quantum and classical phenomena. In condensed matter physics, in particular, scattering mechanisms, loss of quantum information, or breakdown of topological protection are deeply rooted in the intricate details of how and where the dissipation occurs. Despite its vital importance the microscopic behavior of a system is usually not formulated in terms of dissipation because the latter is not a readily measureable quantity on the microscale. Although nanoscale thermometry is gaining much recent interest [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] , the existing thermal imaging methods lack the necessary sensitivity and are unsuitable for low temperature operation required for study of quantum systems. Here we report a superconducting quantum interference nano-thermometer device with sub 50 nm diameter that resides at the apex of a sharp pipette and provides scanning cryogenic thermal sensing with four orders of magnitude improved thermal sensitivity of below 1 µK/Hz 1/2 . The non-contact non-invasive thermometry allows thermal imaging of very low nanoscale energy dissipation down to the fundamental Landauer limit [16][17][18] of 40 fW for continuous readout of a single qubit at 1 GHz at 4.2 K. These advances enable observation of dissipation due to single electron charging of individual quantum dots in carbon nanotubes and reveal a novel dissipation mechanism due to resonant localized states in hBN encapsulated graphene, opening the door to direct imaging of nanoscale dissipation processes in quantum matter. 2 Investigation of energy dissipation on the nanoscale is of major fundamental interest for a wide range of disciplines from biological processes, through chemical reactions, to energy-efficient computing [1][2][3][4][5] . Study of dissipation mechanisms in quantum systems is of particular importance because dissipation demolishes quantum information. In order to preserve a quantum state the dissipation has to be extremely weak and hence hard to measure. As a figure of merit for detection of low power dissipation in quantum systems 16 we consider an ideal qubit operating at a typical readout frequency of 1 GHz. Landauer's principle states the lowest bound on energy dissipation in an irreversible qubit operation to be 0 = B ln 2, where B is Boltzmann's constant and is the temperature 17,18 . At = 4.2 K, 0 = 410 -23 J, several orders of magnitude below 10 -19 J of dissipation per logical operation in present day superconducting electronics and 10 -15 J in CMOS devices 19,20 . Hence the power dissipated by an ideal qubit operating at a readout rate of = 1 GHz will be as low as = 0 = 40.2 fW. The resulting temperature increase of the qubit will depend on its size and the thermal properties of the substrate. For example, a 120 × 120 nm 2 device on a 1 µm thick SiO 2 /Si substrate dissipating 40 fW will heat up by about 3 µK (Fig. 1). Suc...

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.

The dynamics of quantized magnetic vortices and their pinning by materials defects determine electromagnetic properties of superconductors, particularly their ability to carry non-dissipative currents. Despite recent advances in the understanding of the complex physics of vortex matter, the behavior of vortices driven by current through a multi-scale potential of the actual materials defects is still not well understood, mostly due to the scarcity of appropriate experimental tools capable of tracing vortex trajectories on nanometer scales. Using a novel scanning superconducting quantum interference microscope we report here an investigation of controlled dynamics of vortices in lead films with sub-Angstrom spatial resolution and unprecedented sensitivity. We measured, for the first time, the fundamental dependence of the elementary pinning force of multiple defects on the vortex displacement, revealing a far more complex behavior than has previously been recognized, including striking spring softening and broken-spring depinning, as well as spontaneous hysteretic switching between cellular vortex trajectories. Our results indicate the importance of thermal fluctuations even at 4.2 K and of the vital role of ripples in the pinning potential, giving new insights into the mechanisms of magnetic relaxation and electromagnetic response of superconductors.

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...