Gauge invariance of heat and charge transport coefficients*

Transport coefficients have been recently shown to be largely independent of the microscopic representation of the current density of the conserved quantity being transported (charge/mass/energy) [1]. This remarkable gauge invariance has been leveraged to lay down a rigorous density-functional theory of heat transport [1], as well as a general approach to it in solids, that nicely bridges the Boltzmann-Peierls kinetic model, which applies to crystals, and the Allen-Feldman one, which applies to glasses [2]. In the case of charge transport, a combination of gauge invariance and Thouless’ quantisation of particle transport [3] allows one to express the electrical conductivity of a stoichiometric ionic conductor in terms of integer-valued, scalar, and time-independent atomic oxidation numbers, instead of real-valued, tensor, and time-dependent Born charges [4]. The departure of non stoichiometric systems from this picture, due to the existence of localised electron pairs, can be fathomed in terms of topological effects on charge transport [5]. In this talk I will review these concepts and report on some key applications of them to liquids and glasses.

[1] A. Marcolongo, P. Umari, and S. Baroni, Nat. Phys. 12, 80 (2016);
[2] L. Isaeva, G. Barbalinardo, D. Donadio, and S. Baroni, Nat. Commun. 10, 3853 (2019);
[3] D.Thouless, Phys. Rev. B, 27, 6083 (1983);
[4] F. Grasselli and S. Baroni, Nat. Phys. 15, 967 (2019);
[5] P. Pegolo, F. Grasselli, and S. Baroni, Phys. Rev. X, in press.