Perpendicular electronic transport and moir\'{e}-induced resonance in twisted interfaces of three-dimensional graphite

Abstract

We calculate the perpendicular electrical conductivity in twisted three-dimensional graphite (rotationally stacked graphite pieces) by using the effective continuum model and the recursive Green's function method. In the low twist angle regime $(\theta \lesssim 2^\circ)$, the conductivity shows a nonmonotonic dependence with a peak and dip structure as a function of the twist angle. By analyzing the momentum-resolved conductance and the local density of states, this behavior is attributed to the Fano resonance between continuum states of bulk graphite and interface-localized states, which is a remnant of the flat band in the magic-angle twisted bilayer graphene. We also apply the formulation to the high-angle regime near the commensurate angle $\theta \approx 21.8^\circ$, and reproduce the conductance peak observed in the experiment.