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2 TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2 2009

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

Olszewski S., Roliński T.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2009

Vol. 13, No 1-2

99-115

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.

New kind of parameterization applied to the Fermi surface of a crystalline solid. Part II: density of states and lengths of arcs calculated as a check of the theory

Roliński T., Olszewski S.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2009

Vol. 13, No 1-2

117-131

In order to check the validity of parameterization of electron states on the Fermi surfaces developed in the preceding paper, this parameterization is applied to the calculation of some definite crystal properties. The first property is the density of electron states versus energy in simple cubic and body-centered cubic crystal lattices, examined formerly on the basis of the Bloch parameterization of electron states by Jelitto; the other property is the length of some special arcs extended on the surfaces. The parameterizations of both approaches, that of the present paper and that developer on the basis of the Bloch states, are found to give results remaining in remarkable agreement.