Short-range excitonic phenomena in low-density metals

TL;DR

This paper reveals that excitonic effects in low-density metals are significant due to reduced screening at short distances, challenging previous assumptions and highlighting the importance of vertex corrections in theoretical models.

Contribution

It demonstrates the existence of excitonic phenomena in low-density metals through Bethe-Salpeter equation analysis, emphasizing the role of short-range physics and the need for vertex corrections.

Findings

Excitonic effects are significant in low-density metals due to reduced screening.

Low-energy modes exhibit strong, anisotropic electron-hole correlations.

Common approximations like LDA can capture these effects despite their simplicity.

Abstract

Excitonic effects in metals are commonly supposed to be weak, because the Coulomb interaction is strongly screened. We investigate the low-density regime of the homogeneous electron gas, where low-energy collective excitations and ghost modes were anticipated. Using the Bethe-Salpeter equation (BSE), we show that both phenomena exist thanks to reduced screening at short distances. This is not captured by common approximations used in ab initio BSE calculations, but requires vertex corrections that take the fermionic nature of charges into account. The electron-hole wavefunction of the low-energy modes shows strong and very anisotropic electron-hole correlation, which speaks for an excitonic character of these modes. The fact that short-range physics 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.