NEW KIND OF PARAMETERIZATION APPLIED TO THE FERMI SURFACE OF A CRYSTALLINE SOLID. PART I: ELECTRON OBSERVABLES AND CURVATURE PARAMETERS EXAMINED ON THE SURFACE

Abstract

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.