New kind of parameterization applied to the fermi surface of a crystalline solid. Part I: electron observables and curvature parameters examined on the surface

• Autorzy: Olszewski S. , Roliński T.
• Języki publikacji: EN

Abstrakty

EN

A magnetic field applied to a crystalline solid causes the electron states on the Fermi surface to circulate along the orbits located on the planes normal to the applied field. For a sufficiently weak field the separate orbits can cover the whole closed Fermi surface. A suitable parameterization of the states on the orbits should be done in a different way than a conventional parameterization applied for the electron states by Bloch. This new kind of parameterization becomes quite simple when the magnetic field is assumed to be directed parallel to one of the crystallographic axes. Computationally, a new description of the electron states on the Fermi surface becomes on many occasions more flexible in its use than the Bloch's one. The simplifications concern mainly an examination of the curvature parameters of the Fermi surface and extremal properties of the electron observables, for example that of electron velocity. Solely the states in the cubic crystal lattices were considered as examples.

Słowa kluczowe

EN

Fermi surfaces of crystalline solids; electron orbits induced in the magnetic field; curvature properties of the Fermi surfaces

• Wydawca: Politechnika Gdańska
• Czasopismo: TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
• Rocznik: 2009
• Tom: Vol. 13, No 1-2
• Strony: 99--115
• Opis fizyczny: Bibliogr. 26 poz., rys.

Twórcy

autor

Olszewski S.

autor

Roliński T.

• Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland,

Bibliografia

• [1] Sommerfeld A and Bethe H 1933 Handbuch d. Physik Part 2 (Geiger H and Scheel K, Eds), Springer, Berlin, 24
• [2] Mott N F and Jones H 1959 The Theory of Properties of Metals and Alloys, University Press, Oxford
• [3] Reitz J R 1955 Solid State Physics (Seitz F and Turnbull D, Eds), Academic, New York, 1
• [4] Callaway J 1974 Quantum Theory of the Solid State, Part A, Academic, New York
• [5] Van Hove L 1953 Phys. Rev. 89 1189
• [6] Phillips J C 1956 Phys. Rev. 104 1263
• [7] Wannier G H 1959 Elements of Solid State Theory, University Press, Cambridge
• [8] Abrikosov A A 1974 Introduction to the Theory of Normal Metals, Academic, New York
• [9] Lacueva G and Overhauser A W 1986 Phys. Rev. B 33 37
• [10] Zimbovskaya N A 2001 Local Geometry of the Fermi Surface and High-Frequency Phenomena in Metals, Springer, New York
• [11] Landau L Z 1930 Phys. 64 629
• [12] Olszewski S, Rolinski T and Kwiatkowski T 1999 Phys. Rev. B 59 3740
• [13] Vail J M 2003 Topics in the Theory of Solid Materials, Institute of Physics Publishing, Bristol, UK
• [14] Olszewski S and Rolinski T 2007 Intern. J. Quant. Chem. 107 1223
• [15] Chambers R G 1960 The Fermi Surface (Harrison W A and Webb M B, Eds), Wiley, New York
• [16] Slater J C 1967 Quantum Theory of Molecules and Solids, McGraw-Hill, New York, 3
• [17] Kittel C 1987 Quantum Theory of Solids, 2nd Edition, Wiley, New York
• [18] Singleton J 2001 Band Theory and Electronic Properties of Solids, University Press, Oxford
• [19] Suhl H 1989 J. Phys. (Paris) 50 2613
• [20] Jones H 1956 Encyclopedia of Physics (Flugge S, Ed.), Springer, Berlin, 19
• [21] Mattis D C 2006 The Theory of Magnetism Made Simple, World Scientific, New Jersey
• [22] Zawadzki W 1969 Physics of Solids in Intense Magnetic Fields (Haidemanakis E D, Ed.), Plenum, New York
• [23] Lass H 1950 Vector and Tensor Analysis, McGraw-Hill, New York
• [24] Oprea J 1997 Differential Geometry and its Applications, Prentice Hall, New York
• [25] Bronstein I N, Semendjajev K A, Musiol G and Muhlig H 2001 Taschenbuch der Mathematik, 5th Edition, Verlag Harri Deutsch, Frankfurt am Main
• [26] Goursat E 1927 Cours d’Analyse Mathematique, 4th Edition, Gauthier-Villars, Paris, 2