VII. <i>Doublets and triplets in the spectrum produced by external magnetic forces</i>

Zeeman, P.

doi:10.1080/14786449708621028

Cited by 54 publications

(22 citation statements)

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“…The x = 1/B that satisfy equation (26) give all the new maxima and minima in the MO at T = 0. Notice that at zero temperature β → ∞ and equation (26) implies x → x n , as expected.…”

Section: Mo Extrema Shiftmentioning

confidence: 97%

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Influence of temperature on the magnetic oscillations in graphene with spin splitting: a new approach

Escudero¹,

Ardenghi²,

Jasen³

2018

J. Phys.: Condens. Matter

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We analyze the magnetic oscillations (MO) due to the de Haas-van Alphen effect, in pristine graphene under a perpendicular magnetic field, taking into account the Zeeman effect. We consider a constant Fermi energy, such that the valence band is always full and only the conduction band is available. At zero temperature the MO consist of two sawtooth peaks, one for each spin. Both peaks have the same frequency, but different amplitude and phase. We show that, in order to observe the spin splitting in the MO, Fermi energy of about 0.1 eV is required. At low temperatures we obtain that the MO can be expressed as the MO at zero temperature, plus small Fermi-Dirac like functions, each centered around the MO peaks. Using this expression, we show that the spin splitting is observable in the MO only when the thermal energy is smaller than the Zeeman energy. We also analyze the shift of the MO extrema as the temperature increases. We show that it depends on the magnetic field, which implies a broken periodicity at nonzero temperature. Finally, we obtain an analytical expression for the MO envelope. The results obtained could be used to infer temperature changes from the MO extrema shift and vice versa.

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“…The x = 1/B that satisfy equation (26) give all the new maxima and minima in the MO at T = 0. Notice that at zero temperature β → ∞ and equation (26) implies x → x n , as expected.…”

Section: Mo Extrema Shiftmentioning

confidence: 97%

“…The new extrema will be located at x = x l − pδ l , where δ l is the corresponding shift and p = 1(−1) for the maxima (minima). In this way we can rewrite equation (26) as a function of δ l and the considered peak x l :…”

Section: Mo Extrema Shiftmentioning

confidence: 99%

Influence of temperature on the magnetic oscillations in graphene with spin splitting: a new approach

Escudero¹,

Ardenghi²,

Jasen³

2018

J. Phys.: Condens. Matter

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“…Moreover, for each of these sidebands the frequency spacing between the two subpeaks grows larger as |α| increases. The observed sideband splitting leads to energy spectra for the amplified quantum noise that are qualitatively analogous to energy spectra of electrons under the Zeeman splitting of the spectral lines in a gas, which occurs in the presence of a strong magnetic field [31].…”

Section: Impact Of the Amplitude Of The Dispersion Oscillationmentioning

confidence: 92%

Nonlinear parametric resonances in quasiperiodic dispersion oscillating fibers

Finot

Sysoliatin

Wabnitz

2015

Optics Communications

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a b s t r a c tWe numerically study the evolution of the spectrum of parametric resonance or modulation instability sidebands in quasiperiodic dispersion oscillating fibers. We separately consider a linear variation along the fiber of either the spatial period, the average dispersion, or the amplitude of the dispersion oscillation. We found that this linear variation of the dispersion oscillating fiber parameters may provide different novel mechanisms for the splitting of the resonance sideband spectrum, owing to coherent interference between quasi-resonant waves that are generated at different points along the fiber.

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“…In the Landau gauge we have A = −Bye x , and the momentum changes following the Peierls substitution [26] p → p − eA. Considering the Zeeman effect [27], the term µ · B = µ B gBs z /2 is added to H, where s z = 2S z / is the Pauli matrix acting in the spin state. We omit the nearestand next-nearest neighbor Rashba SOIs, denoted as λ R1 and λ R2 in [11], since they are negligible in comparison to the intrinsic SOI λ SO .…”

Section: Energy Spectrummentioning

confidence: 99%

Magnetic oscillations in silicene

Escudero

Ardenghi

Jasen

2018

Journal of Magnetism and Magnetic Materials

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In this work the magnetic oscillations (MO) in pristine silicene at T = 0 K are studied. Considering a constant electron density we obtain analytical expressions for the ground state internal energy and magnetization, under a perpendicular electric and magnetic field, taking in consideration the Zeeman effect. It is found that the MO are sawtooth-like, depending on the change in the last occupied energy level. This leads us to a classification of the MO peaks in terms of the Landau level (LL), valley or spin changes. Using this classification we analyze the MO for different values of the electric field E z . When E z = 0, the energy levels have a valley degeneracy and the MO peaks occur only whenever the last energy level changes its LL and/or spin. When E z = 0, the valley degeneracy is broken and new MO peaks appear, associated with the valley change in the last energy level. By analyzing the MO peaks amplitude it is possible to extract information about the Fermi velocity and the spin-orbit interaction strength. Finally we analyze the MO frequencies, which can also be associated with the change of LL, valley or spin in the last energy level.

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VII. Doublets and triplets in the spectrum produced by external magnetic forces

Cited by 54 publications

References 0 publications

Influence of temperature on the magnetic oscillations in graphene with spin splitting: a new approach

Influence of temperature on the magnetic oscillations in graphene with spin splitting: a new approach

Nonlinear parametric resonances in quasiperiodic dispersion oscillating fibers

Magnetic oscillations in silicene

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