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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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Symmetry 2011, 3(3), 541-563; https://doi.org/10.3390/sym3030541
Received: 21 July 2011 / Accepted: 1 August 2011 / Published: 10 August 2011
(This article belongs to the Special Issue Symmetries of Electronic Order)
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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. View Full-Text
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
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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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