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Abstract:
The reliable prediction of the electrical conductivity from first-principles is important for computationally guided discovery of novel materials with desired electrical properties. Recent studies suggest that improving the accuracy of electrical conductivity calculations in many materials requires accounting for the typically ignored lattice anharmonicity by higher-order electron-phonon interactions. First-principles supercell calculations of the electrical conductivity based on a combination of the Kubo-Greenwood (KG) formula and ab initio molecular dynamics(aiMD) appear to be a promising approach because they naturally include these interactions. However, the application of this approach to crystalline materials has so far received very little attention. This thesis describes the ab initio KG approach, the difficulties of a numerical implementation for crystalline solids, and it demonstrates the problems with two very different systems.
The first case study for silicon (Si), which is a very harmonic material, reveals that the ab initio KG calculations place a high demand on computational resources, and identifies the considerable numerical difficulties. In particular, the KG calcula tion requires a dense k-point sampling, which hinders supercell-size convergence and makes the calculation only feasible with (semi)local density functional approximations (e.g., LDA and GGA). Besides, the necessary introduction of a broadening parameter (η) introduces a significant uncertainty in the quantitative determination of the electrical conductivity. Computationally efficient strategies are discussed in this thesis to address these problems, including: (i) the "scissor operator" approach to correct the LDA band-gap problem; (ii) the “optimal-η scheme" to choose an appropriate value of η; and (iii) the finite-size scaling method to deduce the electrical conductivity in the limit of an infinitely large supercell. With these strategies, it is found that while our calculations at the LDA level yield electrical conductivities in reasonable agreement with experiment, our results do not agree well with those of previous ab initio calculations using the Boltzmann transport equation (BTE) at the LDA level. This comparison suggests that the η problem and the issue of supercellsize convergence still require improved concepts.
The second case study for SnSe, which is a highly anharmonic material, shows very similar numerical difficulties as in the case of Si. For SnSe, it is rather challenging to address the issue of supercell-size convergence, because of the anisotropic electrical conductivity and that the supercell size quickly becomes computationally unfeasible. By choosing appropriate supercell sizes and using the defined strategies, the x and z components of the electrical conductivity in p-doped SnSe at 300 K and 523 K are computed. It is found that at the GGA-PBEsol level the calculated results are in reasonable agreement with experiment. However, the large uncertainties due to the η problem and the issue of supercell-size convergence remain. Comparison with previous ab initio BTE calculations and discussion of the influence of lattice anharmonicity on the supercell-size convergence are presented.
It is concluded that more expertise needs to be acquired on how to deal with the η problem and the issue of supercell-size convergence before the ab initio KG approach can be used to predict the electrical conductivity of crystalline materials.
