Optical absorption in Dirac metals*

I will discuss optical absorption in 2D and 3D Dirac metals due to electron-electron (ee) and electron-hole (eh) interactions within  two models: a Hubbard-like interaction and a dynamically screened Coulomb potentia. The optical conductivity is obtained the summing the leading-order diagrams for the current-current correlation function in the large-N and random-phase approximations. I focus on the range of frequencies below the direct threshold, 0<Ω<2E_F, where absorption is blocked in the non-interacting picture by the Pauli principle. I will that ee and eh scattering processes lead to Ω²lnΩ and Ω² scalings of the conductivity in 2D and 3D, respectively. Above the indirect threshold of E_F, another type of eh processes, similar to Auger-Meitner (AM) processes in atomic physics, starts to contribute. Like in doped semiconductors,  the onset of this contribution is manifested by a threshold singularity. However, the AM singularity in Dirac metals is completely masked by absorption due ee and other eh processes. For Ω~E_F, the effective optical scattering rate due to all processes is of order E_F. Our analytical and numerical calculations show, however, that the proportionality coefficient in the last relation is anomalously small, on the order of 10^-3. This implies that ee and eh interaction in Dirac metals is weaker than it appears to be. Consequences of this finding for Mahan excitons in Dirac metals are also discussed.