  The excitations in graphene and some other materials are described by
two-dimensional massless Dirac equation with applied external potential of some
kind. Solutions of this zero energy equation are built analytically for a wide
class of scalar potentials. In contrast to most publications on analytical
solutions of massless two-dimensional Dirac equation, our potentials really
depend on both spatial coordinates in some bounded domain. Several examples of
such construction are given explicitly.
