Comparison of electron transport calculations in warm dense matter using the Ziman formula

Abstract

The Ziman formulation of electrical conductivity is tested in warm and hot dense matter using the pseudo-atom molecular dynamics method. Several implementation options that have been widely used in the literature are systematically tested through a comparison to accurate but expensive Kohn-Sham density functional theory molecular dynamics (KS-DFT-MD) calculations. The comparison is made for several elements and mixtures and for a wide range of temperatures and densities, and reveals a preferred method that generally gives very good agreement with the KS-DFT-MD results, but at a fraction of the computational cost.PACS numbers: 52.25.Fi, 52.27.Gr * Electronic address: starrett@lanl.gov 1 Hereafter referred to as quantum molecular dynamics (QMD).

Potential of mean force for electrical conductivity of dense plasmas

“…Taking the Fourier Transform of equation (14) and using the definition of the ionic structure factor…”

Kubo–Greenwood approach to conductivity in dense plasmas with average atom models

“…The original ZE formula assumes a free electron DOS and this leads to an ambiguity in the choice of chemical potential and density of scattering electrons. This point was discussed in detail in [14]. The present reformulation recovers the original form of the ZE equation when the DOS goes to the free electron form and removes the ambiguity when the DOS is not free electron like.…”

“…where q 2 = 2p 2 (1 − cos θ), and S(q) is the ion-ion structure factor and dσ/dθ is the differential scattering cross section [14]. p (p ′ ) is the initial (final) momentum of the electron before (after) the collision with the atom.…”

“…Average atom models have been used successfully for many years for equation of state calculations [8][9][10][11][12][13]. They have also been used for electrical conductivity calculations, primarily by coupling to the Ziman-Evans (ZE) formula [14][15][16][17][18][19][20]. Recently, a systemic comparison of calculations of electrical conductivity using this method against Kubo-Greenwood KS-DFT-MD calculations [14] showed generally very good agreement between the methods provided that a judicious choice was made when coupling the average atom model to the ZE formula.…”

Model for the electrical conductivity in dense plasma mixtures

“…The Ziman method is suited to highly degenerate electronic systems, which is not generally the case for plasmas. The Born approximation can lead to large errors in the conductivity for strong scatterers [17]. Other methods, such as the Zubarev generalized linear response method could be used to study the conductivity of mixtures [18,19].…”