Unveiling the Electronic Origin of Anomalous Contact Conductance in Twisted Bilayer Graphene

This study theoretically investigates the contact conductance in twisted bilayer graphene (TBG), addressing recent experimental observations from scanning tunneling microscopy (STM) and conductive atomic force microscopy (c-AFM). These experiments revealed a surprising non-monotonic current pattern as a function of the TBG rotation angle θ, with a peak at θ about 5, a finding that markedly departs from the well-known magic angle TBG behavior. To elucidate this phenomenon, we develop a theoretical and computational framework based on the system's local density of states, and evaluate the contact current over the energy range of states that contribute to the junction. Our results, obtained for both relaxed and rigid TBG structures, indicate that the conductance maximum at θ about 5 is not primarily caused by structural relaxation or by changes in the AA-stacking area: the maximum persists, at essentially the same angle, in rigid (unreconstructed) lattices. Instead, we attribute this peak to the evolution of the electronic band structure, specifically the shifting of van Hove singularities (vHs) toward the Fermi level as the twist angle decreases. The precise location of the maximum tracks the energy window of states participating in the contact, which in contact-mode measurements is set by the local doping under the metallic tip rather than by the small applied bias alone. We show that the angle of maximum conductance shifts with carrier doping, a dependence that is directly testable by electrostatic gating and that a purely structural mechanism cannot produce.