Transparent mirror effect in twist-angle-disordered bilayer graphene

Motivated by recent observations of spatial fluctuations of twist angle in twisted bilayer graphene (TBG) samples, we investigate the effect of such twist angle fluctuations on the transport of Dirac electrons. Variations in twist angle produce spatial modulation of the Fermi velocity as well as a random gauge field. We consider a quasi-one-dimensional model of the disorder, which has a direct analogy with the propagation of light in a medium with a random refractive index. In such situations, Anderson localization of light leads to an exponential decay of transmitted intensity, known as the "transparent mirror effect." In the case of Dirac electrons, however, we show that the localization length depends strongly on the angle of incidence and diverges at a nonzero "Brewster angle". This divergence leads to a power-law decay of the transmission when averaged over incidence angles. Our results have direct implications for the conductivity and the Fano factor of TBG samples. They also suggest a mechanism for disorder-induced collimation, valley filtration, and energy filtration of Dirac electron beams, so that TBG offers a promising new platform for Dirac fermion optics.