The second boundaries of Stability Zones and the angular diagrams of conductivity for metals having complicated Fermi surfaces

Abstract

We consider some general aspects of dependence of magneto-conductivity on a magnetic field in metals having complicated Fermi surfaces. As it is well known, a nontrivial behavior of conductivity in metals in strong magnetic fields is connected usually with appearance of non-closed quasiclassical electron trajectories on the Fermi surface in a magnetic field. The structure of the electron trajectories depends strongly on the direction of the magnetic field and usually the greatest interest is caused by open trajectories that are stable to small rotations of the direction of $\mathbf{B}$. The geometry of the corresponding Stability Zones on the angular diagram in the space of directions of $\mathbf{B}$ represents a very important characteristic of the electron spectrum in a metal linking the parameters of the spectrum to the experimental data. Here we will consider some very general features inherent in the angular diagrams of metals with Fermi surfaces of the most arbitrary form. In particular, we will show here that any Stability Zone actually has a second boundary, restricting a larger region with a certain behavior of conductivity. Besides that, we shall discuss here general questions of complexity of the angular diagrams for the conductivity and propose a theoretical scheme for dividing the angular diagrams into "simple" and "complex" diagrams. The proposed scheme will in fact also be closely related to behavior of the Hall conductivity in a metal in strong magnetic fields. In conclusion, we will also discuss the relationship of the questions under consideration to the general features of an (abstract) angular diagram describing the behavior of quasiclassical electron trajectories at all energy levels in the conduction band.

arXiv comment27 pages, 42 figures, RevTex

References in corpus (9)

• Dynamical Systems, Topology and Conductivity in Normal Metals
• Dynamical Systems, Topology and Conductivity in Normal Metals in strong magnetic fields
• Topological Phenomena in Normal Metals
• Geometry of plane sections of the infinite regular skew polyhedron {4,6|4}
• Diffusion for chaotic plane sections of 3-periodic surfaces
• First-principles generation of Stereographic Maps for high-field magnetoresistance in normal metals: an application to Au and Ag
• On the analytical properties of the magneto-conductivity in the case of presence of stable open electron trajectories on a complex Fermi surface
• Oscillation phenomena and experimental determination of exact mathematical Stability Zones for magneto-conductivity in metals having complicated Fermi surfaces
• Existence and measure of ergodic leaves in Novikov's problem on the semiclassical motion of an electron

Cited by in corpus (3)

• The complexity classes of angular diagrams of the metal conductivity in strong magnetic fields
• Reconstructions of the electron dynamics in magnetic field and the geometry of complex Fermi surfaces
• Quasiperiodic functions on the plane and electron transport phenomena