Measuring the energy-momentum dispersion relation in quantum materials can provide key insights into their strongly correlated electronic phenomena. We have recently demonstrated a new type of a scanning probe microscope – the Quantum Twisting Microscope (QTM) – capable of measuring electrons in momentum space in a similar way to the way a scanning tunneling microscope (STM) measures electrons in real-space. The QTM is based on a van-der-Waals (vdW) heterostructure on a tip, which, when brought into contact with another vdW sample, allows electrons to tunnel into it at many locations quantum coherently. With an extra twist degree of freedom, this microscope becomes a momentum-resolving local scanning probe. The first version of QTM operated at room temperature, and we demonstrated quantum coherence at the tip and directly image the energy bands of monolayer and twisted bilayer graphene. Recently, we generalized the QTM to cryogenic temperatures and use the QTM to image neutral excitations by the momentum resolved inelastic tunneling.

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