Archive for Rational Mechanics and Analysis

, Volume 230, Issue 2, pp 701–733 | Cite as

Thermodynamic Limit of Crystal Defects with Finite Temperature Tight Binding

  • Huajie ChenEmail author
  • Jianfeng Lu
  • Christoph Ortner


We consider a tight binding model for localised crystalline defects with electrons in the canonical ensemble (finite Fermi 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.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesBeijing Normal UniversityBeijingChina
  2. 2.Departments of Mathematics, Physics and ChemistryDuke UniversityDurhamUSA
  3. 3.Mathematics InstituteUniversity of WarwickCoventryUK

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