The complexity classes of angular diagrams of the metal conductivity in strong magnetic fields
arXiv:1902.00290 · doi:10.1134/S1063776119050042
Abstract
We consider angular diagrams describing the dependence of the magnetic conductivity of metals on the direction of the magnetic field in rather strong fields. As it can be shown, all angular conductivity diagrams can be divided into a finite number of classes with different complexity. The greatest interest among such diagrams is represented by diagrams with the maximal complexity, which can occur for metals with rather complicated Fermi surfaces. In describing the structure of complex diagrams, in addition to the description of the conductivity itself, the description of the Hall conductivity for different directions of the magnetic field plays very important role. For the evaluation of the complexity of angular diagrams of the conductivity of metals, it is convenient also to compare such diagrams with the full mathematical diagrams that are defined (formally) for the entire dispersion relation.
arXiv comment24 pages, 32 figures, revtex
References in corpus (10)
- 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
- The second boundaries of Stability Zones and the angular diagrams of conductivity for metals having complicated Fermi surfaces