Anderson Localization and Delocalization of Dirac Electrons in Monolayer Graphene in One-dimensional Random Scalar and Vector Potentials

We study Anderson localization and delocalization of Dirac electrons in monolayer graphene in one-dimensional random scalar and vector potentials theoretically for two different cases. In the first case, the random parts of the scalar and vector potentials are uncorrelated while, in the second case, they are proportional to each other. We calculate the localization length for all values of the disorder strength in a numerically exact manner using the invariant imbedding method and derive analytical expressions for it, which are accurate in the weak disorder region. We also derive the incident angle at which obliquely incident electron waves are completely delocalized. We find that this condition, which includes the ordinary Klein tunneling as a special case, is equivalent to the condition that the effective wave impedance is uniform. In the presence of a vector potential, the delocalization angle can be tuned to nonzero values in contrast to Klein tunneling. We investigate the dependence of the localization length on the disorder strength and find that, in certain cases, the localization length increases monotonically to infinity as the disorder strength increases from zero. We discuss the implications of these results on electron supercollimation and other observable phenomena.