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Quantum topological effects in the transport properties of ionic conductors

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According to the Green-Kubo theory of linear response, the electric conductivity of an extended system is proportional to the time integral of the equilibrium current auto-correlation function. In this talk I will provide an answer to the following silly question: how is it that in ionic insulators a vanishing conductivity results from a non vanishing current? The answer is rooted in the topological quantisation of adiabatic particle transport, a property discovered by Thouless in the early eighties. Thouless’ theory allows one to give a rigorous definition of the atomic oxidation states in extended systems, a concept that, despite its ubiquitousness in chemistry, has long eluded a proper quantum mechanical interpretation. By combining this theory with a gauge invariance principle, recently introduced in the theory of heat transport, I will demonstrate that the substitution of the real-valued, time-dependent, Born effective-charge tensors that enter the quantum-mechanical definition of the ionic current with integer-valued, time-independent, scalar oxidation numbers results in the same electric conductivity, as predicted by the Green-Kubo theory. A few numerical experiments on molten salts will be reported on, demonstrating the soundness of our findings. These findings not only provide an answer to the silly question, but also relieve us from the burden of computing Born effective charges on the fly in ab-initio molecular-dynamics simulations of charge transport in ionic conductors.

This talk is part of the Theory - Chemistry Research Interest Group series.

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