Plasmon and magnetoplasmon excitation in two-dimensional electron space-charge layers on GaAs

Batke, E.; Heitmann, D.; Tu, C. W.

doi:10.1103/physrevb.34.6951

Cited by 156 publications

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“…1 with the firstorder dispersion in k of a magnetoplasmon, ω 2 = ω 2 c + 2πe 2 n s k/(κm * ). Kohn's theorem manifests itself by the fact that only one peak is visible for k → 0 [7], and for finite wave vectors k the magnetoplasmon interacts with harmonics of the cylcotron resonance, resulting in so the called Bernstein modes [16][17][18].To make the Hofstadter subband structure of the Landau bands discernible, we have to resort to short periods L = 50 nm and strong modulation V 0 = 4 meV, just as we had to in order to observe the subbands in the thermodynamic density of states [5]. In addition, the structures are very sensitive to the location of the chemical potential with respect to the subbands, i.e.…”

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Manifestation of the Hofstadter butterfly in far-infrared absorption

Guðmundsson

Gerhardts²

1996

Phys. Rev. B

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The far-infrared absorption of a two-dimensional electron gas with a squarelattice modulation in a perpendicular constant magnetic field is calculated self-consistently within the Hartree approximation. For strong modulation and short period we obtain intra-and intersubband magnetoplasmon modes reflecting the subbands of the Hofstadter butterfly in two or more Landau bands. The character of the absorption and the correlation of the peaks to the number of flux quanta through each unit cell of the periodic potential depends strongly on the location of the chemical potential with respect to the subbands, or what is the same, on the density of electrons in the system. Typeset using REVT E X 1 Indications of the Hofstadter subband structure [1,2] of the Landau bands of a twodimensional electron gas (2DEG) in square modulated lateral superlattices have been believed to be found directly [3] and indirectly [4] in transport measurements. This opens the important question of whether the subband structure can directly be detected in far-infrared (FIR) absorption measurements. Calculations of the ground state properties of the laterally modulated 2DEG indicate that the strong screening effects would hamper an observation of even the coarse structure of the Hofstadter butterfly in, e.g. magnetocapacitance or magnetoresistance measurements, unless very short periods and strong modulation would be used [5]. But what about FIR measurements?The FIR-absorption is determined by the self-consistent field which describes the dynamical screening of the incident external field. Since, as calculations [5] show, screening is also very important in the ground state, screening effects should be treated on equal footing in both the ground state and in the FIR response. That an inconsistent treatment of screening effects may lead to qualitatively wrong results in a 2DEG with strong lateral modulation is known from the case of quantum dots. There, according to the generalized Kohn's theorem [6,7], Coulomb interaction effects on the ground state and dynamical response of a parabolically confined electron system cancel, so that the dot responds at the bare singleelectron frequencies. This experimentally confirmed fact has been reproduced only by those many-body calculations which have treated the interaction effects in the ground state and in the FIR response on the same footing. Results of such calculations have been published for isolated quantum dots [8,9] and for unidirectionally modulated 2DEG [10,11], but to our knowledge no corresponding results are available for the square modulation. 1The square lateral superlattice with period L is spanned by the lattice vectors R = ml 1 + nl 2 , where l 1 = Lx, and l 2 = Lŷ are the primitive translations of the Bravais lattice B; n, m ∈ Z. The reciprocal lattice R is spanned by G = G 1 g 1 + G 2 g 2 , with g 1 = 2πŷ/l 1 , g 2 = 2πx/l 2 , and G 1 , G 2 ∈ Z. The ground-state properties of the interacting 2DEG in a perpendicular homogeneous magnetic field B = Bẑ and the periodic potential V (...

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Manifestation of the Hofstadter butterfly in far-infrared absorption

Guðmundsson

Gerhardts²

1996

Phys. Rev. B

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“…The Bernstein modes are familiar in the physics of gas plasma [6] and 3D solid state plasma [2]. They were also studied both theoretically [7][8][9] and experimentally [10][11][12][13][14] in 2DESs under different conditions including the quantum Hall regime [15,16].…”

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Bernstein modes and giant microwave response of a two-dimensional electron system

Zabolotnykh

2014

Phys. Rev. B

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We report on a contribution to the microwave response of a two-dimensional electron system in a magnetic field which originates from excitation of virtual Bernstein modes. These collective modes emerge as a result of interaction between the usual magnetoplasmon mode and cyclotron resonance harmonics. The electrons are found to experience a strongly enhanced radiation field when its frequency falls in a gap of the Bernstein modes spectrum. This field can give rise to nonlinear effects, one of which, the parametric cyclotron resonance, is discussed. We argue that this resonance leads to a plasma instability in the ultraclean system. The instability-induced heating is responsible for the giant photoresistivity spike recently observed in the vicinity of the second cyclotron resonance harmonic.PACS numbers: 73.21. Fg, 73.20.Mf, 73.43.Qt, 72.30.+q Plasma oscillations are well known; their study began about a century ago by Langmuir and Tonks. These oscillations are mostly investigated in two different types of systems: low-density nondegenerate gas plasma [1] and the degenerate plasma of solids [2]. In the latter case plasma excitations are often referred to as plasmons. A characteristic feature of the solid state systems is that the motion of particles can be easily restricted in one or more directions and thus low-dimensional systems can be created. Properties of plasmons in these systems differ dramatically from those in the three-dimensional (3D) systems. For instance, the plasmon dispersion law in a twodimensional (2D) electron system (ES) can be written as ω (2) p (q) = 2πn s e 2 q/κm, where n s is 2D electron concentration, κ is the surrounding dielectric constant, m is electron effective mass, and q is the 2D wave vector of the plasmon. The spectrum of 2D plasmons is gapless and strongly depends on q in contrast to the dispersionless spectrum of the 3D plasmon ω (3) p (q) = 4πn 3D e 2 /κm, where n 3D is the electron concentration of 3DES.Recently an ultrastrong radiation-plasmon coupling in 2DES in magnetic field has been observed [3,4]. Plasma oscillation in the perpendicular magnetic field B is called the upper hybrid mode in gas plasma or the magnetoplasmon mode in solid state plasma. The dispersion relation of the excitation is as follows:where ω c = eB/mc is the electron cyclotron frequency, and ω (i)p is the plasmon frequency in a 3D (i = 3) or 2D (i = 2) system in the absence of a magnetic field.Plasma oscillations determined by Eq. (1) can interact with cyclotron resonance harmonics due to finite value of qR c , where R c = v F /ω c is the electron cyclotron radius, and v F is the Fermi velocity (in the case of degenerate plasma). This interaction splits mode (1) into the so-called Bernstein modes. In 2DES these modes, see Consider the influence of the Bernstein modes on the screening of incident radiation by magnetoplasmons in 2DES. If a wave vector of radiation q is nonzero and the radiation frequency Ω lies in one of the gaps, see Fig. 1(b), then real magnetoplasma modes are not excited but elect...

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“…The collective excitations in the two-dimensional electron gas with no account of the spin polarization have been studied for a long time [11], [12], including the magnetoplasmons existing in the two-dimensional electron gas located in the external magnetic field [13], [14]. The spin-polarized two-dimensional electron gas exists in the magnetic semiconductors.…”

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Extraordinary waves in two dimensional electron gas with separate spin evolution and Coulomb exchange interaction

Andreev

2017

Physics of Plasmas

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Hydrodynamics analysis of waves in two-dimensional degenerate electron gas with the account of separate spin evolution is presented. The transverse electric field is included along with the longitudinal electric field. The Coulomb exchange interaction is included in the analysis. In contrast with the three-dimensional plasma-like mediums the contribution of the transverse electric field is small. We show the decrease of frequency of both the extraordinary (Langmuir) wave and the spinelectron acoustic wave due to the exchange interaction. Moreover, spin-electron acoustic wave has negative dispersion at the relatively large spin-polarization. Corresponding dispersion dependencies are presented and analyzed.

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Plasmon and magnetoplasmon excitation in two-dimensional electron space-charge layers on GaAs

Cited by 156 publications

References 38 publications

Manifestation of the Hofstadter butterfly in far-infrared absorption

Manifestation of the Hofstadter butterfly in far-infrared absorption

Bernstein modes and giant microwave response of a two-dimensional electron system

Extraordinary waves in two dimensional electron gas with separate spin evolution and Coulomb exchange interaction

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