Ab initio theory of the Drude plasma frequency

Abstract

We derive a theoretical expression to calculate the Drude plasma frequency ω D based on quantum mechanical time-dependent perturbation theory in the long-wavelength regime. We show that, in general, ω D 2 should be replaced by a second-rank tensor, the Drude tensor D , which we relate to the integral over the Fermi surface of the convective momentum flux tensor divided by the magnitude of the Fermi velocity and which is amiable to analytical and numerical evaluation. We also obtain an expression in terms of the average inverse mass tensor. For Sommerfeld’s model of metals, our expression yields the ubiquitous plasma frequency ω D 2 = 4 π n e e 2 / m e . We compare our expressions with those of previous theories. The Drude tensor takes into account the geometry of the unit cell and may be calculated from first principles for isotropic as well as anisotropic metallic systems. We present results for the noble metals Ag, Cu, and Au without stress and subject to isotropic and uniaxial strains; we also compare the results with those available from experiments. We show that, within density functional theory, nonlocal potentials are necessary to obtain an accurate Drude tensor.