Gauge invariance of heat and charge transport coefficients

Transport coefficients in extended systems have been recently demonstrated 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 of transport coefficients has been leveraged to lay down a rigorous density-functional theory of heat transport [1], as well as a general approach to it, valid in the low-temperature regime, that nicely bridges the Boltzmann-Peierls kinetic model, that applies to crystals, and the Allen-Feldman one, that 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 an insulating fluid in terms of integer-valued, scalar, and time-independent atomic oxidation numbers, instead of real-valued, tensor and time-dependent Born charges [3]. 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, Nature Physics 12, 80–84 (2016);
[2] L. Isaeva, G. Barbalinardo, D. Donadio, and S. Baroni, Nat. Commun. 10, 3853 (2019);
[3] D.Thouless, Phys. Rev. B, 27(10), 6083–6087 (1983).
[4] F. Grasselli and S. Baroni, Nature Physics 15, 967–972 (2019).