Thermodynamic Limit of Crystal Defects with Finite Temperature Tight Binding

TL;DR

This paper analyzes the thermodynamic limit of crystal defects within a finite temperature tight binding model, establishing convergence properties and ensemble equivalence as the domain size increases.

Contribution

It proves the limit model for localized crystalline defects at finite temperature converges in the grand-canonical ensemble with a fixed Fermi-level, providing quantitative convergence rates.

Findings

Convergence of nuclei configurations as domain size grows

Fermi-level remains fixed at the homogeneous crystal level

Quantitative rates of convergence established

Abstract

We consider a tight binding model for localised crystalline defects with electrons in the canonical ensemble (finite electronic temperature) and nuclei positions relaxed according to the Born--Oppenheimer approximation. We prove that the limit model as the computational domain size grows to infinity is formulated in the grand-canonical ensemble for the electrons. The Fermi-level for the limit model is fixed at a homogeneous crystal level, independent of the defect or electron number in the sequence of finite-domain approximations. We quantify the rates of convergence for the nuclei configuration and for the Fermi-level.