Momentum-Resolved Spectroscopy of Superconductivity with the Quantum Twisting Microscope

Abstract: We develop a theoretical framework for probing superconductivity with momentum resolution using the quantum twisting microscope (QTM), a planar tunneling device where a graphene tip is rotated relative to a two-dimensional sample. Due to in-plane momentum conservation, the QTM directly measures the superconducting spectral function along well-defined trajectories in momentum space. The relative intensities of electron and hole excitations encode the Bogoliubov coherence factors, revealing the momentum dependence of the pairing magnitude. Three $C_{3z}$-related tunneling channels enable direct detection of rotational symmetry breaking, as well as nodal points in the superconducting order parameter. We apply our framework to superconductivity within the Bistritzer-MacDonald model of noninteracting electrons and the Topological Heavy Fermion model, which accounts for electron-electron interactions. Together, these capabilities establish the QTM as a direct probe of the pairing symmetry and microscopic origin of superconductivity in two-dimensional materials.