On the analytical properties of the magneto-conductivity in the case of presence of stable open electron trajectories on
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RONIC PROPERTIES OF SOLID
On the Analytical Properties of the Magneto-Conductivity in the Case of Presence of Stable Open Electron Trajectories on a Complex Fermi Surface1 A. Ya. Maltsev* Landau Institute for Theoretical Physics, Chernogolovka, Moscow oblast, 142432 Russia *e-mail: [email protected] Received October 6, 2016
Abstract–We consider the electric conductivity in normal metals in presence of a strong magnetic field. It is assumed here that the Fermi surface of a metal has rather complicated form such that different types of quasiclassical electron trajectories can appear on the Fermi level for different directions of B. The effects we consider are connected with the existence of regular (stable) open electron trajectories which arise in general on complicated Fermi surfaces. The trajectories of this type have a nice geometric description and represent quasiperiodic lines with a fixed mean direction in the p-space. Being stable geometric objects, the trajectories of this kind exist for some open regions in the space of directions of B, which can be represented by “Stability Zones” on the unit sphere S2. The main goal of the paper is to give a description of the analytical behavior of conductivity in the Stability Zones, which demonstrates in general rather nontrivial properties. DOI: 10.1134/S1063776117040148
I. INTRODUCTION Our considerations here will be connected with the geometry of the quasiclassical electron trajectories on the Fermi surface in the presence of a strong magnetic field. The main goal of the paper is to give a detailed consideration of the contribution of the stable open trajectories to the conductivity tensor in the limit ωBτ → ∞. As we will see below, in spite of rather regular geometric properties of the stable (generic) open trajectories, their contribution to magneto-conductivity is quite non-trivial from analytical point of view, which is caused by nontrivial statistical properties of the trajectories of this kind. Here we will try to represent a general picture of the magneto-conductivity behavior in the case of presence of such trajectories on the Fermi-surface, including the description of the dependence of conductivity on both the magnitude and the direction of B. As we will see, both the structure of a “Stability Zone” on the angle diagram and the conductivity behavior in strong magnetic fields will demonstrate actually rather non-trivial properties. We will base our considerations on the topological picture for the electron dynamics in the space of the quasi-momenta, arising for general dispersion relation e (p) under the presence of a magnetic field. So, according to standard approach we will assume that the electron states in the conductivity zone are parametrized by the values of the quasimomenta p 1 The article was translated by the author.
which in fact should be considered as points of the three-dimensional space, factorized over the vectors of the reciprocal lattice:
T = R /{n1a1 + n2a 2 + n3a 3}, n1, n2, n3 ∈ Z . 3
3
The basis vectors of the reciprocal lattice a
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