Specificity of $τ$ -- approximation for chaotic electron trajectories on complex Fermi surfaces

Abstract

The work examines a special behavior of the magnetic conductivity of metals that arises when chaotic electron trajectories appear on the Fermi surface. This behavior is due to the scattering of electrons at singular points of the dynamic system describing the dynamics of electrons in $\, {\bf p}$-space, and caused by small-angle scattering of electrons on phonons. In this situation, the electronic system is described by a "non-standard" relaxation time, which plays the main role in a certain range of temperature and magnetic field values.

Figures (12)

• Figure 1: Trajectories of system (\ref{['MFSyst']}) on a periodic Fermi surface of a rather complex shape
• Figure 2: Form of topologically regular open trajectories of system (\ref{['MFSyst']}) in planes orthogonal to ${\bf B}$.
• Figure 3: Angular diagrams of type A (top) and B (bottom) (schematic). The letters "e" and "h" denote the sets of directions ${\bf B}$ corresponding to the presence of only closed trajectories on the Fermi surface and Hall conductivity of a fixed type (electron and hole, respectively).
• Figure 4: The shape of Dynnikov’s chaotic trajectories in planes, orthogonal to ${\bf B}$.
• Figure 5: Examples of cylinders of closed trajectories of system (\ref{['MFSyst']}) on the Fermi surface