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Is tight-binding modelling still relevant?

Date: 18.03.2013
Time: 10:00 a.m.

Patrice Turchi, Lawrence Livermore National Laboratory, Livermore, USA

Within a tight-binding description of the electronic structure a real-space approach for studying the electronic structure and transport properties of materials that exhibit both chemical and topological disorders is presented. First, for a chemically random alloy based on a periodic lattice, it is shown that the Coherent Potential Approximation (CPA) equations can be solved self-consistently in real-space [1] with an extended recursion technique for both diagonal and off-diagonal disorders with the same accuracy as is currently done in reciprocal space. The resulting Green's function is given by a continued fraction expansion, and this analytic form can be conveniently used to determine alloy properties, e.g., electronic density of states, energetics. Second, combined with an orbital peeling technique, I show that this approach can be very efficiently applied to the determination of the effective interactions that build up the configurational part of the total energy within the embedded cluster method. Third, I present a real-space recursion-based approach to the prediction of DC and AC conductivities in chemically disordered alloys within the Kubo-Greenwood formalism. Finally, I will discuss the advantages of this real-space calculation of the Green's function methodology and show that it is applicable to a broad class of generic problems that do not require the accuracy of ab initio electronic structure methodology, and in particular the description of partial disorder in complex alloys and the relation between topological and chemical disorders in amorphous alloys.

Work performed under the auspices of the U.S. DOE by LLNL under Contract DE-AC52-07NA27344.

References:
1. P. Turchi, F. Ducastelle, and G. Tréglia
"Band gaps and asymptotic behavior of continued fraction coefficients"
J. Phys. C: Sol. Stat. Phys. 15, 2891 (1982).

2. P. Turchi, G. Tréglia, and F. Ducastelle
"Electronic structure and phase stability of A15 transition metals and alloys"
J. Phys. F: Met. Phys. 13, 2543 (1984).

3. P. Turchi and F. Ducastelle
"Continued fractions and perturbation theory: application to tight binding systems"
Springer Series in Solid State Sciences, vol. 58 (Springer-Verlag, Berlin), ed. by D. G. Pettifor and D. L. Weaire, 104-119 (1985).

4. A. Gonis, X.-G. Zhang, A. J. Freeman, P. Turchi, G. M. Stocks, and D. M. Nicholson
"Configurational energies and effective cluster interactions in substitutionally disordered binary alloys"
Phys. Rev. B 36, 4630 (1987).

5. P. E. A. Turchi, D. Mayou, and J. P. Julien
"Real-space Tight-binding Approach to Stability and Order in Substitutional Multi-component Alloys"
Phys. Rev. B 56, 1726-1742 (1997).

6. P. E. A. Turchi, D. Mayou, and J. P. Julien
"Real-space Tight-binding Approach to Order in Complex Alloys"
to be published in the Proceedings of the 9th International Conference on Modern Materials and Technologies (CIMTEC'98), ed. by P. Vincenzini (Techna Publishers S.R.L., Faenza, 1998), 83.

7. P. E. A. Turchi, D. Mayou, and J.-P. Julien
"Integrated Quantum-mechanical Approach to Stability, Chemical Order, and Phase Evolution in Complex Alloys"
published in the Proceedings of the International Conference on Solid-Solid Phase Transformations' 99, ed. by M. Koiwa, K. Otsuka, and T. Miyazaki (JIMIC-3) (Japan Institute of Metals, 1999), p. 625-628.

8. J.-P. Julien, P. E. A. Turchi, and D. Mayou
“Real-space Tight-binding Approach to Electronic Structure and Stability in Substitutional Alloys”
Computational Materials Science, 17 (2-4), 217-223 (2000).

9. P. E. A. Turchi and D. Mayou
"Real-space Approach to Electronic Transport in Complex Alloys"
Phys. Rev. B 64, 075113-1 to 9 (2001).

10. J.-P. Julien, P. E. A. Turchi, and D. Mayou
“Real-space Solution of the Coherent Potential Approximation Equations in the Shiba Approximation”
Phys. Rev. B 64, 195119-1 to 16 (2001).

Supporting information:

Special_Turchi.pdf
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