Mischligandenkomplexe einiger Seltener Erden

Rana, H. S.; Tandon, J. P.

doi:10.1007/bf00913613

Cited by 7 publications

(19 citation statements)

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“…The electronic properties of graphene have generated tremendous interest in both experimental and theoretical arenas [2], [4], [5], [6], [7], [8], [9], [12]. The energy dispersion relation of electrons and holes with zero (or close to zero) bandgap results in novel behavior of both singleparticle and collective excitations [1], [2], [4], [5], [6], [7], [8], [9], [12]. The high mobility of electrons in graphene has prompted theoretical and experimental investigations into graphene based ultra high speed electronic devices such as field-effect transistors, pn-junction diodes, and terahertz devices [7], [10], [11], [4], [5], [12], [13], [14].…”

Section: Introductionmentioning

confidence: 99%

“…The energy dispersion relation of electrons and holes with zero (or close to zero) bandgap results in novel behavior of both singleparticle and collective excitations [1], [2], [4], [5], [6], [7], [8], [9], [12]. The high mobility of electrons in graphene has prompted theoretical and experimental investigations into graphene based ultra high speed electronic devices such as field-effect transistors, pn-junction diodes, and terahertz devices [7], [10], [11], [4], [5], [12], [13], [14]. Negative conductance at terahertz frequencies under population inversion conditions has been predicted by Ryzhii et.…”

Section: Introductionmentioning

confidence: 99%

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Graphene Terahertz Plasmon Oscillators

Rana

2008

IEEE Trans. Nanotechnology

476

365

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Abstract-In this paper we propose and discuss coherent terahertz sources based on charge density wave (plasmon) amplification in two dimensional graphene. The coupling of the plasmons to interband electron-hole transitions in population inverted graphene layers can lead to plasmon amplification through stimulated emission. Plasmon gain values in graphene can be very large due to the small group velocity of the plasmons and the strong confinement of the plasmon field in the vicinity of the graphene layer. We present a transmission line model for plasmon propagation in graphene that includes plasmon dissipation and plasmon interband gain due to stimulated emission. Using this model, we discuss design for terahertz plasmon oscillators and derive the threshold condition for oscillation taking into account internal losses and also losses due to external coupling. The large gain values available at terahertz frequencies in graphene can lead to integrated oscillators that have dimensions in the 1-10 µm range.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Graphene Terahertz Plasmon Oscillators

Rana

2008

IEEE Trans. Nanotechnology

476

365

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“…The massless electron spectrum leads to unusual transport and electrodynamic properties, which have been intensively studied in the literature, see e.g. [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31] and for review [32,33].Electrodynamic properties of graphene have been theoretically studied in Refs. [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31].…”

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confidence: 99%

“…[16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]. The frequency dependent conductivity [16,17,20,21,22], as well as plasmon [23,25,27,29,30], plasmon-polariton [24], and transverse electromagnetic wave spectra [31] have been investigated. In all these papers electrodynamic response of the system has been studied within the linear response theory (for instance, using the Kubo formalism, or the random phase approximation, or the self-consistent-field approach).…”

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Non-linear electromagnetic response of graphene

Mikhaǐlov¹

2007

Europhys. Lett.

440

512

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It is shown that the massless energy spectrum of electrons and holes in graphene leads to the strongly non-linear electromagnetic response of this system. We predict that the graphene layer, irradiated by electromagnetic waves, emits radiation at higher frequency harmonics and can work as a frequency multiplier. The operating frequency of the graphene frequency multiplier can lie in a broad range from microwaves to the infrared.In the past two years a great deal of attention has been attracted by a recently discovered, new two-dimensional (2D) electronic system -graphene, built out of a single monolayer of carbon atoms with a honeycomb 2D crystal structure [1,2]. The band structure of the charge carriers in this system consists of six Dirac cones at the corners of the hexagonshaped Brillouin zone [3,4], with the massless, linear electron/hole dispersion. The massless electron spectrum leads to unusual transport and electrodynamic properties, which have been intensively studied in the literature, see e.g. [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31] and for review [32,33].Electrodynamic properties of graphene have been theoretically studied in Refs. [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]. The frequency dependent conductivity [16,17,20,21,22], as well as plasmon [23,25,27,29,30], plasmon-polariton [24], and transverse electromagnetic wave spectra [31] have been investigated. In all these papers electrodynamic response of the system has been studied within the linear response theory (for instance, using the Kubo formalism, or the random phase approximation, or the self-consistent-field approach). In this Letter we show that, apart from all the fascinating and non-trivial properties of graphene predicted and observed so far, this material should also demonstrate strongly non-linear electrodynamic behavior. In particular, irradiation of the graphene sheet by a harmonic electromagnetic wave with the frequency Ω should lead to the emission of the higher harmonics with the frequencies mΩ, m = 3, 5, . . ., from the system. The operating frequency of such a frequency multiplier can vary from microwaves up to infrared, and the required ac electric field is rather low, especially at low carrier densities and low temperatures. The predicted non-linear electrodynamic properties of graphene may open up new exciting opportunities for building electronic and optoelectronic devices based on this material.To qualitatively demonstrate the non-linear behavior of graphene electrons consider a classical 2D particle with the charge −e and the energy spectrum ǫ p = V p = V p 2 x + p 2 y in the external electric field E x (t) = E 0 cos Ωt. Here V is the velocity of 2D electrons in the energy band (in graphene V ≈ 10 8 cm/s [1, 2]). According to the classical equations of motion dp x /dt = −eE x (t) the momentum p x will then be equal to p x (t) = −(eE 0 /Ω) sin Ωt, and the velocity v x = ∂ǫ p /∂p x is then v x (t) = −V sgn(sin Ωt). If there are n s particles per unit area, the corresponding ac ...

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