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The Pauli equations describing electron (hole) dynamics in 2D Dirac-likeintrinsic semiconductors in external (impurity) scalar potential and forinhomogeneous lattice distortions are obtained within second quantizationapproach. We show that the modifying external perturbation terms in formulatedno-pair equations are in general non-local and demonstrates singular behaviorin gapless situation where they do not depend on semiconductor parameters. Itis shown that lattice distortion perturbation can cause confinement of bothelectrons and holes in the same spatial region. The proposed approach isverified by comparison with well-established results in low energy limit. Theconsideration of position operator in second quantization approach allowselucidating the physical meaning of spin-orbit-like and Darwin-like terms.

Pauli equations and non-commutative position operators in 2D Dirac-like semiconductors in view of second quantization