Four-component Dirac–Hartree–Fock (DHF) theory provides a direct framework for treating relativistic effects arising from both one-body and two-body interactions. The one-body Dirac term includes scalar relativity and one-electron spin–orbit coupling, while the relativistic two-electron operator introduces additional scalar-relativistic, spin–orbit, spin–spin, and retardation effects through the Coulomb, Gaunt, and gauge terms. Here, we extend non-periodic DHF to periodic systems by deriving and implementing Kramers-unrestricted DHF with the Dirac–Coulomb (DC), Dirac–Coulomb–Gaunt (DCG), and Dirac–Coulomb–Breit (DCB) Hamiltonians. Applications to polymeric C, Si, Ge, and graphene demonstrate relativistic band-structure and topological calculations within this framework. For graphene, the Dirac-point gap increases from 19.1 μeV with DC-DHF to 43.8 and 43.9 μeV with DCG-DHF and DCB-DHF, respectively, while the Fu–Kane analysis yields a nontrivial ℤ₂ invariant, ν = 1. These results demonstrate the importance of both one-electron and two-electron relativistic effects in determining periodic electronic structure and establish a framework for their direct treatment in solid-state systems.