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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, theta. Although control of the global theta with a precision of about 0.1 degrees has been demonstrated(1-7), 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 state(9) and to map the local theta variations in hexagonal boron nitride (hBN)-encapsulated MATBG devices with relative precision better than 0.002 degrees and a spatial resolution of a few moire periods. We find a correlation between the degree of theta 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 theta 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 theta 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 theta 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.

SQUID-on-tip tomographic imaging of Landau levels in magic-angle graphene provides nanoscale maps of local twist-angle disorder and shows that its properties are fundamentally different from common types of disorder.

Memristor-enabled neuromorphic computing systems provide a fast and energy-efficient approach to training neural networks(1-4). However, convolutional neural networks (CNNs)-one of the most important models for image recognition(5)-have not yet been fully hardware-implemented using memristor crossbars, which are cross-point arrays with a memristor device at each intersection. Moreover, achieving software-comparable results is highly challenging owing to the poor yield, large variation and other non-ideal characteristics of devices(6-9). Here we report the fabrication of high-yield, high-performance and uniform memristor crossbar arrays for the implementation of CNNs, which integrate eight 2,048-cell memristor arrays to improve parallel-computing efficiency. In addition, we propose an effective hybrid-training method to adapt to device imperfections and improve the overall system performance. We built a five-layer memristor-based CNN to perform MNIST10 image recognition, and achieved a high accuracy of more than 96 per cent. In addition to parallel convolutions using different kernels with shared inputs, replication of multiple identical kernels in memristor arrays was demonstrated for processing different inputs in parallel. The memristor-based CNN neuromorphic system has an energy efficiency more than two orders of magnitude greater than that of state-of-the-art graphics-processing units, and is shown to be scalable to larger networks, such as residual neural networks. Our results are expected to enable a viable memristor-based non-von Neumann hardware solution for deep neural networks and edge computing.