Transport and spectral properties of magic angle twisted bilayer graphene junctions based on local orbital models

The electronic properties of junctions defined electrostatically on twisted bilayer graphene can be addressed theoretically using lattice models. Recent works have introduced minimal local orbital models to describe twisted bilayer graphene at the magic angle (MATBLG) with different degrees of approximation and accounting for fragile topology. In the present work we use a Green's function formalism to obtain the spectral and transport properties for MATBLG junctions based on these models. We introduce different symmetry breaking perturbations to simulate the effect of interactions and characterize the topology of the bulk bands by analyzing the corresponding Wilson loops. We then analyze the spectral properties for different types of edges and in the case of a domain wall in the sublattice symmetry breaking parameter. We further consider a three region junction where one could control independently the central and lateral regions doping level. In the limit where the central region is fixed at the charge neutrality point and the lateral ones are heavily doped, the spectral and the two terminal transport properties can be understood in terms of the hybridization of chiral states along the junctions. These properties are found to be extremely sensitive to the orientation of the junctions along the moir\'e lattice.