Scanning probe microscopy (SPM) has facilitated many scientific discoveries utilizing its strengths of spatial resolution, non-destructive characterization and realistic in situ environments. However, accurate spatial data are required for quantitative applications but this is challenging for SPM especially when imaging at higher frame rates. We present a new operation mode for scanning probe microscopy that uses advanced image processing techniques to render accurate images based on position sensor data. This technique, which we call sensor inpainting, frees the scanner to no longer be at a specific location at a given time. This drastically reduces the engineering effort of position control and enables the use of scan waveforms that are better suited for the high inertia nanopositioners of SPM. While in raster scanning, typically only trace or retrace images are used for display, in Archimedean spiral scans 100% of the data can be displayed and at least a two-fold increase in temporal or spatial resolution is achieved. In the new mode, the grid size of the final generated image is an independent variable. Inpainting to a few times more pixels than the samples creates images that more accurately represent the ground truth.

We propose a novel method to detect and correct drift in non-raster scanning probe microscopy. In conventional raster scanning drift is usually corrected by subtracting a fitted polynomial from each scan line, but sample tilt or large topographic features can result in severe artifacts. Our method uses self-intersecting scan paths to distinguish drift from topographic features. Observing the height differences when passing the same position at different times enables the reconstruction of a continuous function of drift. We show that a small number of self-intersections is adequate for automatic and reliable drift correction. Additionally, we introduce a fitness function which provides a quantitative measure of drift correctability for any arbitrary scan shape.

The realization of quantum spin Hall effect in HgTe quantum wells is considered a milestone in the discovery of topological insulators. Quantum spin Hall states are predicted to allow current flow at the edges of an insulating bulk, as demonstrated in various experiments. A key prediction yet to be experimentally verified is the breakdown of the edge conduction under broken time-reversal symmetry. Here we first establish a systematic framework for the magnetic field dependence of electrostatically gated quantum spin Hall devices. We then study edge conduction of an inverted quantum well device under broken time-reversal symmetry using microwave impedance microscopy, and compare our findings to a non-inverted device. At zero magnetic field, only the inverted device shows clear edge conduction in its local conductivity profile, consistent with theory. Surprisingly, the edge conduction persists up to 9 T with little change. This indicates physics beyond simple quantum spin Hall model, including material-specific properties and possibly many-body effects.