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Nanometer-scale imaging of magnetization and current density is the key todeciphering the mechanisms behind a variety of new and poorly understoodcondensed matter phenomena. The recently discovered correlated states hosted inatomically layered materials such as twisted bilayer graphene or van der Waalsheterostructures are noteworthy examples. Manifestations of these states rangefrom superconductivity, to highly insulating states, to magnetism. Theirfragility and susceptibility to spatial inhomogeneities limits theirmacroscopic manifestation and complicates conventional transport ormagnetization measurements, which integrate over an entire sample. In contrast,techniques for imaging weak magnetic field patterns with high spatialresolution overcome inhomogeneity by measuring the local fields produced bymagnetization and current density. Already, such imaging techniques have shownthe vulnerability of correlated states in twisted bilayer graphene totwist-angle disorder and revealed the complex current flows in quantum Halledge states. Here, we review the state-of-the-art techniques most amenable tothe investigation of such systems, because they combine the highest magneticfield sensitivity with the highest spatial resolution and are minimallyinvasive: magnetic force microscopy, scanning superconducting quantuminterference device microscopy, and scanning nitrogen-vacancy centermicroscopy. We compare the capabilities of these techniques, their requiredoperating conditions, and assess their suitability to different types of sourcecontrast, in particular magnetization and current density. Finally, we focus onthe prospects for improving each technique and speculate on its potentialimpact, especially in the rapidly growing field of two-dimensional (2D)materials.

Technical Review: Imaging weak magnetic field patterns on the nanometer-scale and its application to 2D materials