Thermodynamic Limit of Crystal Defects with Finite Temperature Tight Binding
Provides a rigorous mathematical foundation for modeling localized crystal defects in materials science, addressing a known bottleneck in finite-temperature defect simulations.
The paper proves that the thermodynamic limit of a tight binding model for crystal defects with finite electronic temperature converges to a grand-canonical ensemble with a fixed Fermi level, independent of the defect. It quantifies convergence rates for nuclei configuration and Fermi level.
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.