Abstract

The Green-Kubo theory of linear response [1] allows one to extract the static electrical conductivity from the time-correlation function of the charge flux in equilibrium molecular dynamics simulations. While, in a classical-ions picture, the definition of a charge flux is immediate, things are in principle different from an ab-initio perspective, due to the continuous charge distribution of the electrons, and one must rely on the modern theory of polarization (MTP). I combine recently formulated invariance principles of transport coefficients [2] with arguments from charge-transport topological quantization [3] to prove that the same ab initio electrical conductivity of ionic fluids is exactly obtained if the time-dependent Born charge tensors, entering the MTP definition, are replaced by the time-independent integer oxidation numbers of the atoms [4]. Besides providing an alternative method to compute the ab initio electrical conductivity with no need for MTP calculations, this result offers a topology-based definition of oxidation numbers in disordered materials, as I show through numerical experiments on molten potassium chloride. Finally, I discuss non-stoichiometric systems, where quantized charge transport may occur without a net ionic displacement [5].

References:

[1] M. S. Green, J. Chem. Phys. 20(8), 1281 (1952)

[2] A. Marcolongo, P. Umari, and S. Baroni, Nature Physics 12, 80 (2016); review: F. Grasselli and S. Baroni, Eur. Phys. J. B 94 , 160 (2021)

[3] D. J. Thouless, Phys. Rev. B 27 , 6083 (1983)

[4] F. Grasselli and S. Baroni, Nature Physics 15, 967 (2019)

[5] P. Pegolo, F. Grasselli and S. Baroni, Phys. Rev. X 10 , 041031 (2020); review: P. Pegolo, S. Baroni, and F. Grasselli, Ann. Phys. (Berlin) 534, 2200123 (2022)