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V. M. Burdeinyy and V. Kh. Kasiyanenko
«Application of a Method of Conformal Mappings to Examination of an Electronic Spectrum of Vicinal Surfaces»
001–023 (2019)

PACS numbers: 02.30.-f, 68.35.B-, 68.35.Md, 68.49.Jk, 68.65.Cd, 73.20.At, 73.21.Cd

Conformal mapping method is proposed to study electron spectrum of vicinal surfaces formed by periodically ordered arrays of terraces. The Jacobian for the double conformal mapping of system unit cell into the cell with the canonical form is determined. The wave function, dispersion equation and its solutions in the main approximation relative to the small observed values of displacement angle are found.

Keywords: vicinal surface, conformal mapping, Bragg reflection, wave equation, energy spectrum

1. A. Mugarza, F. Shiller, J. Kuntze, J. Cord n, M. Ruiz-Os s, and J. E. Ortega, J. Phys. Condens. Matter, 18: S27 (2006).
2. G. V. Benemanskaya, P. A. Dement'ev, S. A. Kukushkin, M. N. Lapukin, A. V. Osipov, and S. N. Timoshina, Pis'ma v ZhTF, 42, No. 42: 51 (2016).
3. A. A. Kordyuk, Fizika Nizkikh Temperatur, 40, No. 4: 375 (2014).
4. D. Yu. Usachov, A. M. Shikin, A. Yu. Varykhalov, V. K. Adamchuk, and A. Rader, Fizika Tverdogo Tela, 49, No 5: 899 (2007).
5. A. M. Shikin, A. Varykhalov, S. A. Gorovikov, G. V. Prudnikova, V. K. Adamchuk, K.-H. Rieder, W. Guadat, and O. Rader, Journal of Electron Spectroscopy and Related Phenomena, 144-147: 625 (2005).
6. A. Mugarza and J. E. Ortega, J. Phys. Condens. Matter, 15: S3281 (2003).
7. S. Fl gge, Practical Quantum Mechanics I (Berlin-Heidelberg-New-York: Springer-Verlag: 1971).
8. J. Lobo, E. G. Michel, A. R. Bachmann, S. Speller, L. Roca, J. Kuntze, and J. E. Ortega, J. Vac. Sci. Technol., A21, No. 4: 1194 (2003).
9. B. Obreshkov and Th. Uwe, Phys. Rev. A, 74: 012901-10 (2006).
10. Jin-Nam Yeo, Lan-Hee Yang, and B. D. Yu, Journal of the Korean Physical Society, 54, No. 1: 115 (2009).
11. C. Barreteau, F. Raouafi, M. C. Desjonqu res, and D. Spanjaard, ccsd-00002151, version 1 - 25 Jun 2004, 34 p.;
12. M. Roth, M. Pickel, J. Wang, M. Weinelt, Th. Fayster, Appl. Phys., B74: 661 (2002).
13. B. A. Stickler, U. Even, and K. Hornberger, arXiv:1410.7243v.1, [quant-phys], 27 October 2014.
14. L. I. Magarill, A. V. Chaplik, and M. V. Jentin, Uspekhi Fizicheskikh Nauk, 175, No. 9: 95 (2005).
15. D. J. Ben Daniel and C. B. Duke, Phys. Rev., 152: 683 (1966).
16. O. Von Roos, Phys. Rev. B, 27: 7547 (1983).
17. O. Von Roos and H. Mavromatis, Phys. Rev. B, 31: 2294 (1985).
18. R. Ko and S. Saym, J. Phys. A: Math. Theor., 43: 455203 (2010).
19. M. A. Lavrentiev and B. V. Shabat, Metody Teorii Funktsiy Kompleksnoy Peremennoy (Moscow: Nauka: 1987).
20. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integaly i Ryady: Dopolnitel'nyye Glavy (Moscow: Nauka: 1986).
21. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (Eds. M. Abramowitz and I. A. Stegun), Nat'l Bureau of Standards. Appl. Math. Ser. Vol. 55 (Washington, D.C.: U.S. Govt. Printing Office: 1964).
22. N. W. Ashcroft and N. D. Mermin, Solid State Physics (New York-Chicago-San Francisco-Atlanta-Dallas-Montreal-Toronto-London-Sydney: Holt, Rinehart and Winston: 1976).
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