Oxidation states, Thouless' pumps, and nontrivial transport in nonstoichiometric electrolytes*

Thouless' quantization of adiabatic particle transport permits to associate an integer topological charge with each atom of an electronically gapped material. Under suitable conditions, they provide a rigorous definition of oxidation states and atoms can be identified as integer-charge carriers in electrolytes [1]. In these conditions, charge transport is convective, i.e. it cannot occur without substantial ionic flow.
We show that the topological requirements that allow these conditions to be broken are the same that would determine a Thouless' pump mechanism if the system were subject to a suitably defined time-periodic Hamiltonian. This determines a nontrivial transport regime whereby charge can flow without any ionic convection, even in electronic insulators.
We demonstrate these results on simple molecular models displaying a quantum-pump mechanism; then, we examine nonstoichiometric alkali-halide melts, where the nontrivial transport regime is such that most of the total charge current is uncorrelated from the ionic ones [2].

[1] FG and SB, Nat. Phys. 15, 967-972 (2019)
[2] PP, FG and SB, PRX (in press), arXiv:2006.16749 (2020)