  A topological transition in high-temperature superconductors FeTe1-xSex,
occurring at a critical range of Se concentration x, underlies their intrinsic
topological superconductivity and emergence of Majorana states within vortices.
Nonetheless, the influence of Se concentration and distribution on the
electronic states in FeTe1-xSex remains unclear, particularly concerning their
relationship with the presence or absence of Majorana states. In this study, we
combine density functional theory (DFT) calculations, pz-dxz/yz-based and
Wannier-based Hamiltonian analysis to systematically explore the electronic
structures of diverse FeTe1-xSex compositions. Our investigation reveals a
nonlinear variation of the spin-orbit coupling (SOC) gap between pz and dxz/yz
bands in response to x, with the maximum gap occurring at x = 0.5. The pz-pz
and dx2-y2-pz interactions are found to be critical for pd band inversion.
Furthermore, we ascertain that the distribution of Se significantly modulates
the SOC gap, thereby influencing the presence or absence of Majorana states
within local vortices.
