Intrinsic optical absorption in Dirac metals

Abstract

A Dirac metal is a doped (gated) Dirac material with the Fermi energy (EF) lying either in the conduction or valence bands. In the non-interacting picture, optical absorption in gapless Dirac metals occurs only if the frequency of incident photons (Ω) exceeds the direct (Pauli) frequency threshold, equal to 2EF. In this work, we study, both analytically and numerically, the role of electron–electron (ee) and electron–hole (eh) interactions in optical absorption of two-dimensional (2D) and three-dimensional (3D) Dirac metals in the entire interval of frequencies below 2EF. We show that, for Ω≪EF, the optical conductivity, ℜσ(Ω), arising from the combination of ee and certain eh scattering processes, scales as Ω2lnΩ in 2D and as Ω2 in 3D, respectively, both for short-range (Hubbard) and long-range (screened Coulomb) interactions. Another type of eh processes, similar to Auger–Meitner (AM) processes in atomic physics, starts to contribute for Ω above the direct threshold, equal to EF. Similar to the case of doped semiconductors with parabolic bands studied in prior literature, the AM contribution to ℜσ(Ω) in Dirac metals is manifested by a threshold singularity, ℜσ(Ω)∝(Ω−EF)d+2, where d is the spatial dimensionality and 0<Ω−EF≪EF. In contrast to doped semiconductors, however, the AM contribution in Dirac metals is completely overshadowed by the ee and other eh contributions. Numerically, ℜσ(Ω) happens to be small in almost the entire range of Ω<2EF. This finding may have important consequences for collective modes in Dirac metals lying below 2EF.