Short-Range Excitonic Phenomena in Low-Density Metals

Excitonic effects in metals are usually supposed to be weak, because the Coulomb interaction is strongly screened. Here, we investigate the low-density regime of the homogeneous electron gas, where, besides the usual high-energy plasmons, the existence of low-energy excitonic collective modes has recently been suggested. Using the Bethe-Salpeter equation (BSE), we show that indeed low-energy modes appear, thanks to reduced screening at short distances. This requires going beyond common approximations to ab initio BSE calculations, which suffer from a self-polarization error that overscreens the electron-hole interaction. The electron-hole wave function of the low-energy mode shows strong and very anisotropic electron-hole correlation, which speaks for an excitonic character of this mode. The fact that the electron-hole interaction at short distances is at the origin of these phenomena explains why, on the other hand, also the simple adiabatic local density approximation to time-dependent density functional theory can capture these effects. This exotic regime might be found in doped semiconductors and interfaces.