We present a $GW$ space-time algorithm for periodic systems in a Gaussian basis including spin-orbit coupling. We employ lattice summation to compute the irreducible density response and the self-energy, while we employ $k$-point sampling for computing the screened Coulomb interaction. Our algorithm enables accurate and computationally efficient quasiparticle band structure calculations for atomically thin transition-metal dichalcogenides. For monolayer ${\mathrm{MoS}}_{\text{2}}, {\mathrm{MoSe}}_{\text{2}}, {\mathrm{WS}}_{\text{2}}$, and ${\mathrm{WSe}}_{\text{2}}$, computed $GW$ band gaps agree on average within 50 meV with plane-wave-based reference calculations. $G_0{W}_0$ band structures are obtained in less than two days on a laptop (Intel i5, 192 GB RAM) or in less than 30 minutes using 1024 cores. Overall, our work provides an efficient and scalable framework for $GW$ calculations on atomically thin materials.

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• Spin-orbit coupling
• Transition metal dichalcogenides
• Band structure methods
• Density functional theory
• GW method