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Symmetry 2011, 3(3), 541-563; doi:10.3390/sym3030541

Symmetry Aspects of the Band Structure and Motion Equations Applied in Calculating the Cyclotron Frequency of Electrons in Metals

Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, Warsaw, Poland
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Received: 21 July 2011 / Accepted: 1 August 2011 / Published: 10 August 2011
(This article belongs to the Special Issue Symmetries of Electronic Order)
Download PDF [414 KB, 11 August 2011; original version 10 August 2011]

Abstract

Cyclotron frequency of a crystal electron is, in general, not an easily accessible parameter. Nevertheless, its calculation can be simplified when the symmetry properties of the band structure and those of the motion equations in the magnetic field are simultaneously taken into account. In effect, a combined symmetry of the electron Hamiltonian and that of the Lorentz equation provide us with a non-linear oscillator problem of high symmetry. In the next step, the kinetic energy of the oscillator can be separated from the whole of electron energy and applied in a new kind of calculation of the cyclotron frequency which is much more simple than before. In consequence, a detailed approach to the electron circulation, also in more complex band structures, becomes a relatively easy task. For different crystal lattices of cubic symmetry taken as examples the cyclotron frequency of the present and a former method are compared numerically giving the same results.
Keywords: band structure symmetry; Lorentz equation; crystal electrons; Hamilton equations; metals; cyclotron frequency band structure symmetry; Lorentz equation; crystal electrons; Hamilton equations; metals; cyclotron frequency
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Olszewski, S.; Roliński, T. Symmetry Aspects of the Band Structure and Motion Equations Applied in Calculating the Cyclotron Frequency of Electrons in Metals. Symmetry 2011, 3, 541-563.

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