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.