  We study Anderson localization of massless Dirac electrons in two dimensions
in one-dimensional random scalar and vector potentials theoretically for two
different cases, in which the scalar and vector potentials are either
uncorrelated or correlated. From the Dirac equation, we deduce 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 theory, we also develop a numerical method to calculate the
localization length exactly for arbitrary strengths of disorder. In addition,
we derive analytical expressions for the localization length, which are
extremely accurate in the weak and strong disorder limits. In the presence of
both scalar and vector potentials, the conditions for total transmission and
complete delocalization are generalized from the usual Klein tunneling case. We
find that the incident angles at which electron waves are either completely
transmitted or delocalized can be tuned to arbitrary values. When the strength
of scalar potential disorder increases to infinity, the localization length
also increases to infinity, both in uncorrelated and correlated cases. The
detailed dependencies of the localization length on incident angle, disorder
strength and energy are elucidated and the discrepancies with previous studies
and some new results are discussed. All the results are explained intuitively
using the concept of wave impedance.
