  The invention of scanning probe microscopy has revolutionized the way
electronic phenomena are visualized. While present-day probes can access a
variety of electronic properties at a single location in space, a scanning
microscope that can directly probe the quantum mechanical existence of an
electron at multiple locations would provide direct access to key quantum
properties of electronic systems, so far unreachable. Here, we demonstrate a
conceptually new type of scanning probe microscope - the Quantum Twisting
Microscope (QTM) - capable of performing local interference experiments at its
tip. The QTM is based on a unique van-der-Waals tip, allowing the creation of
pristine 2D junctions, which provide a multitude of coherently-interfering
paths for an electron to tunnel into a sample. With the addition of a
continuously scanned twist angle between the tip and sample, this microscope
probes electrons in momentum space similar to the way a scanning tunneling
microscope probes electrons in real space. Through a series of experiments, we
demonstrate room temperature quantum coherence at the tip, study the twist
angle evolution of twisted bilayer graphene, directly image the energy bands of
monolayer and twisted bilayer graphene, and finally, apply large local
pressures while visualizing the evolution of the flat energy bands of the
latter. The QTM opens the way for novel classes of experiments on quantum
materials.
