Transport across twist angle domains in moir\'e graphene

Many of the experiments in twisted bilayer graphene (TBG) differ from each other in terms of the details of their phase diagrams. Few controllable aspects aside, this discrepancy is largely believed to be arising from the presence of a varying degree of twist angle inhomogeneity across different samples. Real space maps indeed reveal TBG devices splitting into several large domains of different twist angles. Motivated by these observations, we study the quantum mechanical tunneling across a domain wall (DW) that separates two such regions. We show that the tunneling of the moir\'e particles can be understood by the formation of an effective step potential at the DW. The height of this step potential is simply a measure of the difference in twist angles. These computations lead us to identify the global transport signatures for detecting and quantifying the local twist angle variations. In particular, Using Landauer-B\"uttiker formalism we compute single-channel conductance ($dI/dV$) and Fano factor for shot noise (ratio of noise power and mean current). A zero-bias, sub-meV transport gap is observed in the conductance which scales with the height of the step potential. One of the key findings of our work is that transport in presence of twist angle inhomogeneity is "noisy", though sub-Poissonian. In particular, the differential Fano factor peaks near the van Hove energies corresponding to the domains in the sample. The location and the strength of the peak is simply a measure of the degree of twist angle inhomogeneity.
Comment: 17 pages, 14 figures