Ultra-complex conductivity diagrams in the nearly free electron approximation

Abstract

We investigate the possibility of the emergence of ultra-complex conductivity diagrams in the nearly free electron approximation for metals with cubic symmetry. Estimates show that the emergence of such diagrams requires the Fermi level to fall into very narrow energy intervals within the conduction band. In our view, this circumstance is mostly due to the high symmetry and the simplest analytical form of the dispersion relations $ε({\bf p})$ under consideration.

Figures (23)

• Figure 1: Complex Fermi surface in $\, {\bf p}$ - space.
• Figure 2: (a) Abstract orientable surfaces of genus $\, g \, = \, 0, 1, 2, 3, 4 \,$. (b) Examples of Fermi surfaces of rank 0, 1, 2 and 3.
• Figure 3: (a) Trajectories of the system (\ref{['MFSyst']}) on the Fermi surface of a rather complex shape. (b) Closed trajectories of the system (\ref{['MFSyst']}). (c) Open periodic trajectories of the system (\ref{['MFSyst']}).
• Figure 4: (a) Stable open trajectory of system (\ref{['MFSyst']}) in a plane orthogonal to $\, {\bf B} \,$. (b) Stability Zones corresponding to different integer planes $\, \Gamma_{\alpha} \,$ on the conductivity diagram (schematically).
• Figure 5: Evolution of Stability Zones on the conductivity diagram in the interval $\, \epsilon_{F} \in \left( \epsilon^{\cal A}_{1} , \, \epsilon^{\cal A}_{2} \right) \,$ (schematically). The signs e and h mark the regions of electron and hole Hall conductivity, respectively.