Charge and heat transport in ionic conductors

Transport coefficients relate the off-equilibrium flow of locally conserved quantities, such as charge, energy, and momentum, to gradients of intensive thermodynamic variables in the linear regime. Despite their mathematical formalization dating back to the middle of the last century, when Green and Kubo developed linear response theory, some conceptual subtleties were only recently understood through the formulation of the gauge-invariance and convective-invariance principles. In a nutshell, these invariance principles suggest that transport coefficients are mostly independent of the microscopic definition of the densities and currents. In this thesis, we analyze the consequences of gauge and convective invariances on the charge and heat-transport properties of ionic conductors. The combination of gauge invariance with Thouless' theorem on charge quantization reconciles Faraday's picture of ionic charge transport---whereby each atom carries a well-defined integer charge---with a rigorous quantum-mechanical definition of atomic oxidation states. The latter are topological invariants depending on the paths traced by the coordinates of nuclei in the atomic configuration space. When some general topological conditions are relaxed, we show that oxidation states lose their meaning, and charge can be adiabatically transported across macroscopic distances without a net ionic displacement. This allows for a classification of the different regimes of ionic transport in terms of the topological properties of the electronic structure of the conducting material. Invariance principles also allow one to compute thermal conductivity in multicomponent materials such as ionic conductors through equilibrium molecular dynamics simulations. In particular, heat management is of paramount importance in solid-state electrolytes, solid materials relevant for the production of next-generation batteries, where ionic conduction is mediated by diffusing vacancies and defects. The aforementioned conceptual difficulties in the theory of thermal transport are the root cause of a lack of systematic exploration of such properties in solid-state electrolytes. We showcase the ability of the invariance principles to overcome these issues together with state-of-the-art data analysis techniques in the paradigmatic example of the Li-ion conductor Li3ClO. We provide a simple rationale to explain the temperature and vacancy-concentration dependence of its thermal conductivity, which can be interpreted as the result of the interplay of a crystalline component and a contribution from the effective disorder generated by ionic diffusion.