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Dynamical Systems, Topology and Conductivity in Normal Metals
New observable integer-valued numbers of the topological origin were revealed
by the present authors studying the conductivity theory of single crystal 3D
normal metals in the reasonably strong magnetic field (). Our
investigation is based on the study of dynamical systems on Fermi surfaces for
the motion of semi-classical electron in magnetic field. All possible
asymptotic regimes are also found for based on the topological
classification of trajectories.Comment: Latex, 51 pages, 14 eps figure
Topological Phenomena in Normal Metals
This paper is devoted to topological phenomena in normal metals with rather
complicated Fermi surface. The results of the article are based on the deep
topological theorems concerning the geometry of non-compact plane sections of
level surfaces of periodic function in 3-dimensional Euclidean space which are
the quasi-classical electron orbits in the presence of homogeneous magnetic
field. The main result is that the observation of electrical conductivity in
strong magnetic fields can reveal such nontrivial topological characteristics
of Fermi surface as integral planes, connected with conductivity tensor and
locally stable under small rotations of magnetic field. This planes are
connected with generic non-closed orbits on the Fermi surface. Some non-generic
situations are also discussed.Comment: 21 pages, 9 Encapsulated Postscript figure
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