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

Paolo Pegolo1*, Federico Grasselli1,2*, Stefano Baroni1,3*

1 SISSA—Scuola Internazionale Superiore di Studi Avanzati, 34136 Trieste, Italy

2 COSMO—Laboratory of Computational Science and Modelling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland

3 CNR—Istituto Officina dei Materiali, SISSA, 34136 Trieste, Italy

* Corresponding authors emails:,,
DOI10.24435/materialscloud:jg-km [version v1]

Publication date: Oct 13, 2020

How to cite this record

Paolo Pegolo, Federico Grasselli, Stefano Baroni, Oxidation states, Thouless' pumps, and nontrivial ionic transport in nonstoichiometric electrolytes, Materials Cloud Archive 2020.118 (2020), doi: 10.24435/materialscloud:jg-km.


Thouless’ quantization of adiabatic particle transport permits to associate an integer topological charge with each atom of an electronically gapped material. If these charges are additive and independent of atomic positions, they provide a rigorous definition of atomic oxidation states and atoms can be identified as integer-charge carriers in ionic conductors. Whenever these conditions are met, charge transport is necessarily convective, i.e. it cannot occur without substantial ionic flow, a transport regime that we dub trivial. 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. The occurrence of these requirements determines a non-trivial transport regime whereby charge can flow without any ionic convection, even in electronic insulators. These results are first demonstrated with a couple of simple molecular models that display a quantum pump mechanism upon introduction of a fictitious time dependence of the atomic positions along a closed loop in configuration space. We finally examine the impact of our findings on the transport properties of non-stoichiometric alkali-halide melts, where the same topological conditions that would induce a quantum pump mechanism along certain closed loops in configuration space also determine a non-trivial transport regime such that most of the total charge current results to be uncorrelated from the ionic ones. In this record we collect the time series of the electric currents, displaced dipoles, and energy band gaps supporting the plots and relevant results supporting our findings.

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634.1 KiB Data to be analyzed to reproduce the relevant results of the paper.
194.8 KiB Jupyter notebook with the code to analyze the data.
1.8 KiB Readme file.
1.5 KiB matplotlib style used by the jupyter notebook.


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Transport properties Thouless' pump Solvation Charge transport MaX

Version history:

2020.127 (version v2) Oct 21, 2020 DOI10.24435/materialscloud:p8-k3
2020.118 (version v1) [This version] Oct 13, 2020 DOI10.24435/materialscloud:jg-km