Far-infrared spectroscopy of quantum wires and dots, breaking Kohn’s theorem

Heitmann, D.; Bollweg, K.; Guðmundsson, Viðar; Kurth, T.; Riege, S. P.

doi:10.1016/s1386-9477(97)00044-1

Cited by 57 publications

(32 citation statements)

References 32 publications

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“…Indeed, in previous studies of traditional 2DEG quantum dot with the shape of the dots deviating from the circular shape, higher order edge modes were observed 8,11,23 , obviously due to the anharmonic confinement introduced by the dot geometry. However, the higher order mode observed in our graphene disks does not evolve into an edge mode in a magnetic field, which is different from the first order mode as well as other higher order modes observed previously in the traditional 2DEG quantum dots 8,23 . This mode is a second order dipolar mode which was previously predicted by theory 17 .…”

Section: Main Textmentioning

confidence: 91%

“…Unlike metal plasmons 19 , the graphene plasmon is expected to be strongly affected by an external magnetic field due to a comparable cyclotron frequency [20][21][22] and plasmon frequency. The effects of a perpendicular magnetic field on the plasmons in conventional 2DEG systems have been extensively studied [7][8][9][10][11]17,23,24 . A major focus of these studies has been localized plasmons in disks 7 and submicron size quantum dots 8,17,23 .…”

Section: Main Textmentioning

confidence: 99%

“…In our case, the typical wavelength is one order of magnitude larger than the graphene disk diameter, and the dipole approximation is satisfied. Appearance of the higher order mode is therefore an indication of the breakdown of Kohn's theorem 23 .…”

Section: Main Textmentioning

confidence: 99%

“…The effects of a perpendicular magnetic field on the plasmons in conventional 2DEG systems have been extensively studied [7][8][9][10][11]17,23,24 . A major focus of these studies has been localized plasmons in disks 7 and submicron size quantum dots 8,17,23 .Here we report the first study of magneto-plasmons in micron size disk arrays of graphene-a different kind two dimensional system. We find that the plasmon lifetime can be dramatically modified by a magnetic field.…”

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confidence: 99%

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Infrared Spectroscopy of Tunable Dirac Terahertz Magneto-Plasmons in Graphene

et al. 2012

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Abstract:Boundaries and edges of a two dimensional system lower its symmetry and are usually regarded, from the point of view of charge transport, as imperfections. Here we present a first study of the behavior of graphene plasmons 1-6 in a strong magnetic field that provides a different perspective. We show that the plasmon resonance in micron size graphene disks 4,6 in a strong magnetic field splits into edge and bulk plasmon modes 7-12 with opposite dispersion relations, and that the edge plasmons at terahertz frequencies develop increasingly longer lifetimes with increasing magnetic field, in spite of potentially more defects close to the graphene edges. This unintuitive behavior is attributed to increasing quasi-one dimensional field-induced confinement and the resulting suppression of the back-scattering 13 .Due to the linear band structure of graphene 14,15 , the splitting rate of the edge and bulk modes develops a strong doping dependence, which differs from the behavior of traditional semiconductor two-dimensional electron gas (2DEG) systems 7,8,11,16 .We also observe the appearance of a higher order mode indicating an anharmonic confinement potential 17 even in these well-defined circular disks. Our work not only 2 opens an avenue for studying the physics of graphene edges, but also supports the great potential of graphene for tunable terahertz magneto-optical devices. Main text:Plasmon excitations in graphene are currently attracting great attention [1][2][3][4][5][6]12 . This is primarily due to the high carrier mobility and the tunable carrier density, which make graphene a promising plasmonic material in the far infrared and terahertz frequency ranges 1,2,5,6,18 . Unlike metal plasmons 19 , the graphene plasmon is expected to be strongly affected by an external magnetic field due to a comparable cyclotron frequency 20-22 and plasmon frequency. The effects of a perpendicular magnetic field on the plasmons in conventional 2DEG systems have been extensively studied [7][8][9][10][11]17,23,24 . A major focus of these studies has been localized plasmons in disks 7 and submicron size quantum dots 8,17,23 .Here we report the first study of magneto-plasmons in micron size disk arrays of graphene-a different kind two dimensional system. We find that the plasmon lifetime can be dramatically modified by a magnetic field. This is especially true for the edge mode, which develops a much longer lifetime than that at zero field. This behavior is counterintuitive since imperfections of the edges may introduce more scattering and decrease the plasmon lifetime. To the best of our knowledge, this is the first demonstration of magnetic field tuning of plasmon lifetime in the terahertz frequency range.Large area graphene disk arrays on SiO 2 /Si are fabricated using standard electron beam lithography and dry etching techniques (for details, see Methods) 6 . Fig. 1a shows a 3 scanning electron micrograph of a sample with a 3-micron diameter (d = 3 m) disk array arranged in a triangular lattice, where the lattice constan...

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Section: Main Textmentioning

confidence: 91%

Section: Main Textmentioning

confidence: 99%

Section: Main Textmentioning

confidence: 99%

mentioning

confidence: 99%

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Infrared Spectroscopy of Tunable Dirac Terahertz Magneto-Plasmons in Graphene

et al. 2012

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“…Consequently, a large number of theoretical investigations have been carried out in this area in the last two decades taking the confinement potential as parabolic [5]. Since most of the quantum dot structures available today are made of polar semiconductors, and the electron-phonon interaction energy scale is almost comparable to the other energy scales of the problem, there have also been several investigations on the polaronic effects in parabolic semiconductor quantum dots and a good deal of literature [6] has already piled up on this subject.However, in recent years a few groups [7] have observed that their experimental results do not support the validity of the generalized Kohn theorem in quantum dots. Rather, their observations suggest that the confining potential is non-parabolic and should be in the form of a finite well.…”

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confidence: 97%

Quantum size effect on the phonon-induced Zeeman splitting in a GaAs quantum dot with Gaussian and parabolic confining potentials

Mukhopadhyaya

Boyacıoğlu

Sağlam

et al. 2008

Physica E: Low-dimensional Systems and Nanostructures

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The Zeeman splitting of the ground and the first excited level of a Gaussian GaAs quantum dot is studied in the presence of electron-longitudinal-optical (LO)-phonon interaction incorporating the spin of the electron and is compared with the case of a parabolic dot. It is shown that the Zeeman splitting is suppressed because of the polaronic interaction and becomes strongly size dependent, but the parabolic confinement overestimates this Zeeman suppression. It is also shown that although the energy levels are split because of the spin-field interaction, the cyclotron frequencies and the Zeeman lines are independent of the electron spin in the dipole transition. The subject of quantum dots has remained in the focus of attention for the last three decades or so for both academic and practical reasons [1]. In this context, semiconductor quantum dot structures have drawn particular attention for their potential applications in nano-semiconducting and optoelectronic devices like single electron transistors, quantum dot lasers, ultra-fast computers and so on. Several early experiments [2], and subsequent theoretical investigations [3] have revealed that Kohn's theorem [4] or more precisely a generalization of it is valid in a quantum dot which suggested that the confining potential would be parabolic in such a system. Consequently, a large number of theoretical investigations have been carried out in this area in the last two decades taking the confinement potential as parabolic [5]. Since most of the quantum dot structures available today are made of polar semiconductors, and the electron-phonon interaction energy scale is almost comparable to the other energy scales of the problem, there have also been several investigations on the polaronic effects in parabolic semiconductor quantum dots and a good deal of literature [6] has already piled up on this subject.However, in recent years a few groups [7] have observed that their experimental results do not support the validity of the generalized Kohn theorem in quantum dots. Rather, their observations suggest that the confining potential is non-parabolic and should be in the form of a finite well. This has provided a renewed impetus in the research of the electronic energy spectra and the associated phenomena in quantum dots. Using a three-dimensional (3D) spherical rectangular potential well of finite depth, Szafran et al. [8] and Bednarek et al. [9] have been able to successfully describe, albeit qualitatively, the charging of quantum dots. Subsequently, Szafran et al. [10] have quantitatively explained the capacitance-spectroscopy data for selfassembled quantum dots simulating the confining potential ARTICLE IN PRESS www.elsevier.com/locate/physe 1386-9477/$ -see front matter r

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Adiabatic Switching Among Quantum Dot Eigenstates: Role of Anharmonicity and Gaussian White Noise

Roy¹,

Arif

Ghosh

2021

Physica Status Solidi (b)

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Current study inquires the time‐dependent quantum adiabatic switching (TDQAS) among the quantum dot (QD) eigenstates under the aegis of Gaussian white noise (GWN) with special emphasis on anharmonicity that may be present in the QD potential. The initial and the final eigenstates are distinguished by different values of magnetic field strength, confinement potential, anisotropy, and anharmonicity. The QAS has been conducted using four different switching functions (SFs), e.g., square, exponential, sinusoidal, and logarithmic. The time development of switching has been monitored with the help of overlap function and quantum information entropy (QIE). The SFs appear to recover the eigenstates of QD corresponding to the final Hamiltonian. The switching paths comprise features such as enhancement, depletion, maximization, minimization, and crossover of the overlap function and entropy. These characteristics of switching paths depend on presence/absence of noise, its pathway of application (additive/multiplicative), and symmetry (odd/even) of the anharmonic potential. The dependence on the type of SF used, however, has been found to be not much significant unless the exclusive role of noise strength on switching path is observed. The study merits importance in view of immense technological applications of QD‐based systems where the noise‐anharmonicity interplay may be exploited to a great extent.

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Far-infrared spectroscopy of quantum wires and dots, breaking Kohn’s theorem

Cited by 57 publications

References 32 publications

Infrared Spectroscopy of Tunable Dirac Terahertz Magneto-Plasmons in Graphene

Infrared Spectroscopy of Tunable Dirac Terahertz Magneto-Plasmons in Graphene

Quantum size effect on the phonon-induced Zeeman splitting in a GaAs quantum dot with Gaussian and parabolic confining potentials

Adiabatic Switching Among Quantum Dot Eigenstates: Role of Anharmonicity and Gaussian White Noise

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