Linear response of an inhomogeneous electron gas

This work describes a calculation of the density response function of an electron gas subject to a one-dimensional sinusoidal potential Ū cos(Q⋅r). We present a first-principles formulation of the wave-vector- and frequency-dependent noninteracting susceptibility ${\chi }^0$(q,q’;ω), based on a Green’s-function approach where the susceptibility χ corresponding to the interacting electron system can be related to ${\chi }^0$ using ideas from density-functional theory. Numerical results are presented for the static noninteracting susceptibility which are seen to exhibit structure associated with the Fermi wave vector ${\mathrm{k}}_F$ as well as the potential wave vector Q. Preliminary numerical results are also presented for χ and the linear density response to a point-charge impurity with electron-electron interactions treated in the random-phase approximation. Possible applications of these results to problems which require a more realistic model of metals beyond the uniform electron gas are discussed.