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Many of the experiments in twisted bilayer graphene (TBG) differ from eachother in terms of the details of their phase diagrams. Few controllable aspectsaside, this discrepancy is largely believed to be arising from the presence ofa varying degree of twist angle inhomogeneity across different samples. Realspace maps indeed reveal TBG devices splitting into several large domains ofdifferent twist angles. Motivated by these observations, we study the quantummechanical 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 theformation of an effective step potential at the DW. The height of this steppotential is simply a measure of the difference in twist angles. Thesecomputations lead us to identify the global transport signatures for detectingand quantifying the local twist angle variations. In particular, UsingLandauer-B\"uttiker formalism we compute single-channel conductance ($dI/dV$)and Fano factor for shot noise (ratio of noise power and mean current). Azero-bias, sub-meV transport gap is observed in the conductance which scaleswith the height of the step potential. One of the key findings of our work isthat transport in presence of twist angle inhomogeneity is "noisy", thoughsub-Poissonian. In particular, the differential Fano factor peaks near the vanHove energies corresponding to the domains in the sample. The location and thestrength of the peak is simply a measure of the degree of twist angleinhomogeneity.

Transport across twist angle domains in moir\'e graphene