Effects of momentum-dependent self-energy in the electronic structure of correlated materials

We study how the $\mathbf{k}$ dependence in the self-energy affects the quasiparticle band structure and one-particle spectral functions. It is known that, in electron-gas-like materials, the self-energy depends significantly on $\mathbf{k}$ and there is a strong cancellation between the $\mathbf{k}$ dependence and the energy dependence of the self-energy. Analysis of the $GW$ self-energy reveals that, even in correlated materials with narrow bands, such as ${\mathrm{SrVO}}_{3}$, the self-energy significantly depends on $\mathbf{k}$. When the nonlocal effect is neglected, the quasiparticle band structure is over-renormalized, yielding too large mass enhancement compared to the case of k-dependent self-energy. The present result suggests that partial cancellation between the frequency dependence and the k dependence in the self-energy is important when discussing the quasiparticle band structure of correlated materials.