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Cyclotron Frequencies and Quanta of the Landau Levels in Semiconductors Having Ellipsoidal Fermi Surfaces Studied in Dependence on Direction of the Magnetic Field

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Olszewski S., Roliński T.

vol. 126

issue 6

1304-1311

A method of calculating the Landau levels in crystals having the ellipsoidal Fermi surfaces has been presented with an accent put on the directional dependence of the energy quanta defined by the levels. Physically the problem concerns mainly semiconductors examined in a nearly-free electron approximation. In this case the shape of the Fermi surface is defined by three different effective masses entering the electron Hamiltonian. Beyond of the masses the method, which can be applied for an arbitrary direction of the magnetic field, does contain no empirical parameters in its framework.

The Hofstadter Diagram Analyzed in Terms of the Band Structure Parameters for a Planar Metal

100%

Roliński T., Olszewski S.

Acta Physica Polonica A

2006

vol. 109

issue 6

753-759

It is demonstrated that a wing of the Hofstadter diagram calculated for the tightly-bound s-electrons in the simple cubic lattice can be reproduced by the dispersion figure of the wave-vector square considered for the electron states of the same lattice, on the condition that the states having equal energies are taken into account. The dispersion splitting increases systematically with the distance of the states from the Brillouin zone center. A similar wing due to dispersion of the electron momentum is calculated also for the s-electron states in the body-centered cubic lattice.

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2 Acta Physica Polonica A

1 2014

1 2006

2 Olszewski S.

2 Roliński T.

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Cyclotron Frequencies and Quanta of the Landau Levels in Semiconductors Having Ellipsoidal Fermi Surfaces Studied in Dependence on Direction of the Magnetic Field

The Hofstadter Diagram Analyzed in Terms of the Band Structure Parameters for a Planar Metal