Fourier analysis applied to cyclotron resonance in metals having anisotropic Fermi surfaces

Olszewski, S.; Roliński, T.; Kwiatkowski, T.

doi:10.1103/physrevb.59.3740

Cited by 19 publications

(96 citation statements)

References 63 publications

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“…The accordance of the expansions in Table 1 with those calculated formally with aid of other methods [11] becomes evident. A physical cyclotron frequency is obtained when ω latt of Table 1 is multiplied by a factor presented in (16); see the end of Section 1.…”

Section: Cyclotron Oscillation Periods and Frequenciessupporting

confidence: 64%

“…This expansion is equal to that calculated earlier with the aid of more conventional, but also more complicated, methods [11].…”

Section: Cyclotron Oscillation Periods and Frequenciesmentioning

confidence: 99%

“…A characteristic point of (19)- (21) is that beyond the symmetry properties dictated by the crystal potential [see (11)- (13)], a supplementary symmetry in the dynamic variables x and p x , namely that due to (9) and (10), occurs in the formalism. In effect of that symmetry, the Hamiltonians (19), (20) and (21) provide us with an anharmonic oscillator problem [11]. The oscillators of this kind are one-dimensional, because x and p x refer to the motion in a single dimension, say, that extended along the axis x.…”

Section: Crystal Hamiltonians As the Oscillator Problemsmentioning

confidence: 99%

“…The constant terms of 1 and 3 are introduced in order to make (11), (12) and (13) at small k x , k y and k z proportional to the free-electron expression:…”

Section: The Formalismmentioning

confidence: 99%

“…This way is much more simple than a former one [11] in which the oscillation frequencies, or time periods, are obtained either from the action function, or from a direct solution of the differential equation of an oscillator. Moreover, the motion parameters of a crystal electron oscillating upon the action of the magnetic field, for example the electron velocity dx dt , can be easily examined for any electron position within the oscillation limits (22).…”

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confidence: 99%

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

Olszewski

Roliński

2011

Symmetry

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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.

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Section: Cyclotron Oscillation Periods and Frequenciessupporting

confidence: 64%

“…This expansion is equal to that calculated earlier with the aid of more conventional, but also more complicated, methods [11].…”

Section: Cyclotron Oscillation Periods and Frequenciesmentioning

confidence: 99%

Section: Crystal Hamiltonians As the Oscillator Problemsmentioning

confidence: 99%

“…The constant terms of 1 and 3 are introduced in order to make (11), (12) and (13) at small k x , k y and k z proportional to the free-electron expression:…”

Section: The Formalismmentioning

confidence: 99%

mentioning

confidence: 99%

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

Olszewski

Roliński

2011

Symmetry

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Ensembles of Electron States in Cubic Lattices Quantized in the Presence of a Magnetic Field

Olszewski

Baszczak

2002

phys. stat. sol. (b)

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PACS: 71.15.Dx; 71.70.Di; 73.43.Cd Quantization of the Landau levels and their density versus energy in cubic crystal lattices are examined for the case of weak and strong magnetic fields. Bands of the tightly-bound s-electron states are chosen as examples of the calculations. With the assumption of a constant phase taken in the quantization process, the density of the Landau levels calculated for weak magnetic fields is found practically identical with the planar density of the Bloch states derived in each lattice case. Simultaneously, the frequency of the electron gyration in the lattice due to the action of the external magnetic field becomes proportional to the reciprocal value of the density of the Landau states. For strong magnetic fields the Roth phase and its connection with the Berry phase are also examined. Repercussions of the applied theory to the quanta of the weak-field Hall conductivity are demonstrated.

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Dispersion of parameters characterizing the Landau levelsin crystals with cubic symmetry

Olszewski¹,

Baszczak

Kozak

2003

Physica Status Solidi (b)

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PACS 71.15. Dx, 71.70.Di Broadening of the Landau levels due to the presence of a crystal cubic lattice is examined on a semiclassical basis for not too strong magnetic fields. The energies of the Landau levels remain discrete also in case of the presence of the lattice potential, but an essential broadening occurs in the momentum space of the electron motion when this motion is limited to a plane being transversal to the applied field. The broadening in the momentum space, attained without any electron-electron interaction admitted for the Landau levels, is described in terms of the band structure parameters characteristic for the presence of the magnetic field. Moreover, for a magnetic field tilted to the crystallographic axes, the broadening is dependent on the inclination angle of the field. Different crystal lattices exhibit different kinds of dispersion. In particular, for the Landau levels of tightly-bound s-electrons in a simple cubic and body-centred cubic lattice there is no dispersion in the electron gyration frequency and degeneracy number of the level area over the value of the wavevector component parallel to the magnetic field. On the other hand, this kind of dispersion exists in the case of the face-centred cubic lattice.

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Fourier analysis applied to cyclotron resonance in metals having anisotropic Fermi surfaces

Cited by 19 publications

References 63 publications

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

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

Ensembles of Electron States in Cubic Lattices Quantized in the Presence of a Magnetic Field

Dispersion of parameters characterizing the Landau levelsin crystals with cubic symmetry

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