First-principles study of electronic transport and structural properties of Cu$_{12}$Sb$_4$S$_{13}$ in its high-temperature phase

TL;DR

This study uses first-principles calculations to analyze the structural and electronic transport properties of high-temperature tetrahedrite Cu$_{12}$Sb$_4$S$_{13}$, revealing insights into its doping mechanisms and thermoelectric behavior.

Contribution

It introduces a novel ab initio approach combining molecular dynamics and the Kubo-Greenwood formula to accurately predict transport properties in complex, anharmonic thermoelectric materials.

Findings

Seebeck coefficient matches experimental data.

Electrical resistivity trend aligns with experiments.

Lorenz number is significantly lower than free-electron value.

Abstract

We present an ab initio study of the structural and electronic transport properties of tetrahedrite, Cu$_{12}$Sb$_4$S$_{13}$, in its high-temperature phase. We show how this complex compound can be seen as the outcome of an ordered arrangement of S-vacancies in a semiconducting fematinite-like structure (Cu3SbS4). Our calculations confirm that the S-vacancies are the natural doping mechanism in this thermoelectric compound and reveal a similar local chemical environment around crystallographically inequivalent Cu atoms, shedding light on the debate on XPS measurements in this compound. To access the electrical transport properties as a function of temperature we use the Kubo-Greenwood formula applied to snapshots of first-principles molecular dynamics simulations. This approach is essential to effectively account for the interaction between electrons and lattice vibrations in such a complex crystal structure where a strong anharmonicity plays a key role in stabilising the high-temperature phase. Our results show that the Seebeck coeffcient is in good agreement with experiments and the phonon-limited electrical resistivity displays a temperature trend that compares well with a wide range of experimental data. The predicted lower bound for the resistivity turns out to be remarkably low for a pristine mineral in the Cu-Sb-S system but not too far from the lowest experimental data reported in literature. The Lorenz number turns out to be substantially lower than what expected from the free-electron value in the Wiedemann-Franz law, thus providing an accurate way to estimate the electronic and lattice contributions to the thermal conductivity in experiments, of great significance in this very low thermal conductivity crystalline material.