Landau level transitions in doped graphene in a time dependent magnetic field

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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“…where M = M V + M C is the net magnetization at zero temperature, given by equation (13). Equation (21)…”

Section: Mo At Nonzero Temperaturementioning

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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“…For a classical electron gas these levels are equidistant, due to the parabolic dispersion relation. For a relativistic-like electron gas, as in graphene, the Landau levels are not equidistant, which is one of the reasons why the Quantum Hall effect can be observed in graphene at room temperatures [8,9,10,11,12,13]. Moreover, the Landau levels create an oscillating behavior in the thermodynamics potentials.…”

Section: Introductionmentioning

confidence: 99%

Ground state magnetization of conduction electrons in graphene with Zeeman effect

Escudero

Ardenghi

Sourrouille

et al. 2017

Journal of Magnetism and Magnetic Materials

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In this work we address the ground state magnetization in graphene, considering the Zeeman effect and taking into account the conduction electrons in the long wavelength approximation. We obtain analytical expressions for the magnetization at T = 0, where the oscillations given by the de Haas van Alphen (dHvA) effect are obtained. We find that the Zeeman effect modifies the magnetization by introducing new peaks associated with the spin splitting of the Landau levels. These peaks are very small for typical carrier densities in graphene, but become prominent for higher densities. The results obtained provide insight of the way in which the Zeeman effect modifies the magnetization, which can be useful to control and manipulate the spin degrees of freedom.

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“…Because H only depends on the y coordinate, we can express the wave function as ψ = e −ikx ( ψ A ψ B ), with ψ A/B depending only on y. Then, introducing the ladder matrices σ ± = σ x ± iσ y and making the change of variable [28]…”

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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Landau level transitions in doped graphene in a time dependent magnetic field

Cited by 11 publications

References 33 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

Ground state magnetization of conduction electrons in graphene with Zeeman effect

Magnetic oscillations in silicene

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