Thermodynamics and Energy Spectrum of Strongly Correlated Proton and Ionic Conductors

Abstract

We describe proton and ionic conductors with lattice models. For proton conductors with hydrogen bonds we use the orientational-tunneling model that takes into account the proton transfer in the spirit of two-stage Grotthuss mechanism as well as the short-range interaction between protons. When simplified this model is reduced to the well-known spinless fermion model. In our investigation we focus on the role of short-range correlations between protons (ions) that may affect the behaviour of the system considerably. In frames of the projected coherent potential approximation we calculate the energy spectrum of the system in one-dimensional case. It consists of one or several energy bands depending on correlation strength. At half filling the system is in the insulating state when correlations are strong and is in the quasi-metallic state when correlations are weak. At certain range of parameters values we also observe the insulator-metal-like transition in the spectrum as it closes the gap with the temperature increase while the system exits in the charge-ordered state. This fact can be considered as theoretical explanation of superionic transition, i.e. transition from the low-temperature ordered (ferroelastic) state to high temperature conducting state with random distribution of ions (protons). We test the results with numerical calculations on finite clusters using exact diagonalization technique.