$\cos^2\theta$ dependence for all energy in a weak vector potential. More recently, the localization behavior of pseudospin-1 and pseudospin-1/2 Dirac particles in disordered superlattices with a random scalar potential was studied in Ref. 20. The localization length was reported to have a $\sin^{-2}\theta$ dependence for all energy and to increase to large values in the strong disorder regime.

In this paper, we consider the continuum Dirac equation in 2D with 1D random scalar and vector potentials, which are characterized by $\delta$-function correlations. In addition to the model where the scalar and vector potentials are independent, we also consider the one where they are strongly correlated. All of our numerical results are essentially exact for all strengths of disorder. Our main focus is to obtain the generalized condition for total transmission and those for complete delocalization in our random models and to understand them in an intuitive and physical way.

We study our problem using three different approaches. Starting from the Dirac equation, we deduce an analytical expression for the effective wave impedance, using which we derive the condition for total transmission and those for delocalization in our random models analytically. Based on the invariant imbedding method (IIM) for solving wave 