  The Pauli equations describing electron (hole) dynamics in 2D Dirac-like
intrinsic semiconductors in external (impurity) scalar potential and for
inhomogeneous lattice distortions are obtained within second quantization
approach. We show that the modifying external perturbation terms in formulated
no-pair equations are in general non-local and demonstrates singular behavior
in gapless situation where they do not depend on semiconductor parameters. It
is shown that lattice distortion perturbation can cause confinement of both
electrons and holes in the same spatial region. The proposed approach is
verified by comparison with well-established results in low energy limit. The
consideration of position operator in second quantization approach allows
elucidating the physical meaning of spin-orbit-like and Darwin-like terms.
