Self-consistent static-density-response function of a metal surface in density-functional theory

Abstract

We obtain the static-linear-density-response function of the conduction electrons in a metal slab in a self-consistent-field approximation derived from density-functional theory. Exchange and correlation effects are included within the local-density-functional (LDF) approximation. The jellium model is used for the periodic ionic background. The response function is obtained by solving a matrix equation for the coefficients of a double-cosine Fourier-series representation for the response. Our solution holds for all values of the two-dimensional wave-vector transfer parallel to the surface $q_{\mathrm{para}}$. The entire surface-screening problem is basically reduced to carrying out matrix algebra on the computer. Our method provides a good approximation for the response function of a semi-infinite medium. We test the method by computing the electron density induced by an impurity placed in the surface region. The singularity of the response function for $q_{\mathrm{para}}$=2$k_F$ ($k_F$ being the Fermi wave vector) gives rise to long-range lateral oscillations in the induced density. The amplitude of these oscillations becomes vanishingly small when the impurity is placed outside the jellium. The oscillations in the induced density along the surface normal are also studied. We quantify the importance of exchange and correlation effects in the response function by comparing the results obtained in the LDF and random-phase approximations.