Experimental observation of edge magnetoplasma excitations in a two-dimensional electron system in the quantum-hall-effect regime

New low-frequency modes corresponding to acoustic edge magnetoplasma excitations have been observed in the resonance microwave absorption spectra of a two-dimensional electron system in a transverse magnetic field. The additional excitation modes have been shown to appear only in the quantum-Hall-effect regime (in narrow magnetic-field regions near the integer values of the filling factor), when the resonance microwave absorption lines exhibit sharp narrowing. The absolute values of the resonance absorption frequencies and their dependence on the parameters of the electron system coincide (without any fitting parameters) with the respective theoretical predictions of the formula describing the properties of the acoustic modes of edge magnetoplasma excitations.     

Dimensional magnetoplasma resonance of 2D holes in (001) GaAs/AlGaAs quantum wells

Dimensional magnetoplasma resonance is observed and studied in a spatially confined, two-dimensional hole system in (001) GaAs/AlGaAs single quantum wells. From the analysis of the field dependence of the magnetoplasma resonance on the diameter of the 2D system, the semiclassical cyclotron hole mass is determined. Its value is found to be equal to 0.26m ₀ (m ₀ is the free electron mass), which considerably exceeds the theoretically predicted value. A method is proposed for a direct determination of the concentration and mobility of 2D holes from the analysis of the magnetoplasma resonance.     

Collective magnetoplasma excitations in two-dimensional electron rings

The spectra of magnetoplasma excitations in two-dimensional electron disks and rings are studied by optical detection of resonance microwave absorption. For ring-shaped structures, two types of edge magnetoplasma modes localized along the inner and outer boundaries of the ring are observed. It is shown that the interaction between these modes leads to a strong modification of their magnetic-field dependences as compared to disks. In addition to the longitudinal edge magnetoplasma excitations, transverse plasma modes associated with the electron density oscillations along the ring radius are revealed. The spectra of magnetoplasma excitations are calculated in terms of the electrodynamic theory for both ring-shaped and disk-shaped structures. The classification of all modes of collective magnetoplasma excitations observed in the experiment is performed on the basis of the comparison between experimental and theoretical results.     

Study of edge magnetoplasma excitations in two-dimensional electron systems with various edge depletion profiles

Resonant microwave absorption by two-dimensional electrons has been measured using coplanar and strip methods. The influence of the edge of a two-dimensional system on the dispersion of edge magnetoplasmons has been studied. It has been found that the edge width can be varied within wide limits (by almost two orders of magnitude) by changing the etching depth of the crystal. It has been shown that the edge of the electron system in the case of etching through the quantum well has a width of about 0.2 μm, whereas the edge in the case of shallow etching (e.g., down to the donor layer) is smooth and can be as wide as 12 μm. The influence of a logarithmic factor, depending on the edge width of the electron system, on edge magnetoplasma excitations dispersion has been studied.     

Coexistence of collective and single-particle effects in the photoresponse of a 2D electron gas to microwave radiation

The photoresponse of magnetoresistance of a high-density two-dimensional electron system to microwave electromagnetic radiation is studied. The damping of the Shubnikov-de Haas oscillation by radiation with a non-monotonic dependence of this effect on the magnetic field and the radiation-induced oscillations of magnetoresistance are observed. The damping is most pronounced within isolated narrow magnetic field intervals that closely correspond to the expected positions of magnetoplasma resonances in the sample under study and also near the cyclotron resonance position. A “window” is observed in the photoresponse near the field value predicted on the basis of a single-particle electron spectrum consisting of broadened Landau levels. The radiation-induced oscillations, the window in the photoresponse, and the damping of the Shubnikov-de Haas oscillations near the cyclotron resonance are described in terms of the theory based on the concept of the nonequilibrium filling of single-electron states. Thus, it is demonstrated that the photoresponse pattern observed in the experiment is formed by both single-particle and collective (magnetoplasma) effects.     

Observation of acoustic edge magnetoplasmons near the filling factor ν = 1

Investigation of acoustic edge magnetoplasma excitations in micrometer two-dimensional electron disks has been carried out. It has been shown that additional acoustic edge magnetoplasma modes associated with the existence of incompressible strips in the two-dimensional electron system caused by Zeeman spin splitting can appear in the system at temperatures below the Zeeman energy. The magnetic dispersion of the first “spin” branch of acoustic edge magnetoplasmons has been studied. It has been shown that this mode vanishes as the filling factor ν = 1 is approached. The dependence of the relative amplitude of acoustic edge magnetoplasmons on the filling factor has also been investigated.     

Universal relation between hall conductivity and the damping constant of edge magnetoplasma resonances

The spectra of edge magnetoplasma excitations in two-dimensional (2D) electron disks have been analyzed by the method of optical detection of resonant microwave absorption. The magnetic dispersion of an edge magnetoplasmon in samples with a high 2D electron density is found to be poorly reproduced by existing theoretical models. Analysis of the magnetic-field dependence of the linewidth of resonant microwave absorption for samples with various 2D electron densities shows that the inverse width of the main mode of resonant microwave absorption is universally proportional to the Hall resistance of 2D electrons.     

Plasma waves in a two-dimensional electron system laterally screened by a metallic gate

The dispersion of magnetoplasma and plasma excitations in two-dimensional electron systems, whose edges are formed by a voltage applied to a metallic gate, has been studied. A substantial decrease in the plasma wave frequency as compared to the plasma frequency measured in the etched mesas with the same geometry, size, and electron density has been observed. The dependence of the observed frequency softening on the structure size has been studied and the laterally screened plasma excitation has been shown to violate the square-root dispersion relation.     

Magnetoplasma modes of a spatially periodic two-dimensional electron gas

We examine the magnetoplasma dispersion of a two-dimensional electron gas with a spatially periodic charge density. The system studied is a periodic array of two-dimensional electron gas strips with constant equilibrium density. The integral equation describing the charge fluctuations on the strips, has been derived and solved numerically. The spatial dependence of the form of either propagating or evanescent waves. The latter are associated with the edge modes, recently discovered in electrons on liquid⁴ He. For a periodic array of two-dimensional strips, the modes in different strips, interact and form bands.     

Magnetoplasma oscillations of a two-dimensional electron layer in a bounded system

The spectrum of magnetoplasma oscillations of a two-dimensional electron layer in a transversal magnetic field is studied under the condition that the electron system is unbounded along the layer plane and screened in the perpendicular direction. It is shown that under certain conditions oscillation frequencies much lower than the electron cyclotron frequency exist. Also the electromagnetic wave-guided oscillations in the system are described. It is shown that a strong magnetic field causes a frequency shift and splitting, depending inversely on the external magnetic field and the transversal specific dimension.     

Observation of plasma and magnetoplasma resonances of two-dimensional electrons in a single MgZnO/ZnO heterojunction

The magnetoluminescence of the two-dimensional electron system in a single Mg _x Zn_{1 ? x} O/ZnO hetero-junction (x = 0.02) at a temperature of 0.3 K in magnetic fields up to 14 T has been studied. The concentration of two-dimensional electrons in the structure under study has been determined from the oscillations of the luminescence intensity as a function of the magnetic field. The value thus obtained is close to the one derived from transport measurements. The resonance corresponding to plasma excitations of two-dimensional electrons has been observed using optical detection of microwave absorption. In a magnetic field, the lower branch of magnetoplasma excitations, which corresponds to the propagation of edge magnetoplasmons in a structure with nearly square geometry, has been observed and investigated.     

Spectrum of polariton excitations of a two-dimensional electron plasma in a magnetic field

Polariton excitations associated with magnetoplasma and cyclotron oscillations in a two-dimensional (2D) electron plasma are studied. In contrast to previous works by other authors, it is concluded that there exists a low-frequency nontransmission band in the spectrum of 2D surface magnetoplasma polaritons. Radiative polariton excitations associated with nonuniform cyclotron oscillations of electrons in a 2D system are investigated. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 3, 200–204 (10 August 1998)     

Cyclotron spin-flip mode in the extreme quantum limit

In a two-dimensional electron system, the combined excitation (the cyclotron spin-flip mode) associated with changes in both orbital and spin quantum numbers is investigated. The energy of the cyclotron spin-flip mode is studied as a function of the electron filling factor. Comparative dependences of the decay times of the cyclotron spin-flip mode and the magnetoplasmon are measured. It is shown that, as the filling factor increases from v = 0 or decreases from v = 1, the damping of the cyclotron spin-flip mode increases significantly, while the magnetoplasma mode remains undamped.     

Magnetoplasma spectra of two-dimensional electron rings

A hydrodynamical approach is employed to study the collective excitations of a two-dimensional electron gas confined in a ring geometry, under a normal magnetic held. The theory predicts a rich spectrum of magnetoplasma excitations, with several branches of high- and low-frequency resonances. It is shown that the low-frequency resonances can be identified as edge magnetoplasmons localized at the inner and outer boundaries of the ring, exhibiting their characteristic antidot-like and dot-like features. The high-frequency resonances are essentially bulk two-dimensional magnetoplasmons. Our calculated magnetoplasma modes and their associated induced charge densities and dipole moments are compared with a recent experiment, and it is found that most of the experimentally observed features of the spectrum are accounted for with the present theory.     

Electrons in bismuth

A review of the electronic properties of pure bismuth is given. Theoretical ideas on the band structure of bismuth and the dispersion relation for electrons near the bottom of the conduction band are briefly outlined. The experiments considered are those which give the most precise information on the Fermi surface (quantum effects in conductivity, cyclotron resonance, size effects, magnetoplasma waves, etc.) and on the electron energy spectrum near the bottom of the conduction band (studies in the quantum limit, infra-red magneto-reflection). The validity of the Cohen model as a first approximation to the electron spectrum in bismuth is established, and deviations from this model are described. Experiments are proposed which may give additional information on electrons in bismuth.     

Transport and cyclotron resonance theory for GaAs-AlGaAs heterostructures

A theory for static and dynamic transport of a two-dimensional electron gas in GaAs-AlGaAs heterostructures at temperature zero is presented. Charged impurities, separated from the electron gas by a spacer layer, are considered as the dominant scattering mechanism. Finite extension of the wave function of the two-dimensional electron gas is taken into account. Multiple scattering effects are included and are shown to lead to a metal insulator transition at low electron densities. Due to plasmon dynamics the scattering is strongly frequency dependent, and this dissipative process determines the width of the cyclotron resonance. The corresponding reactive effect determines the shift of the cyclotron resonance. It is shown that a correlation between line width maximum and zero frequency shift of the cyclotron mode exists, in agreement with experimental results.     

Interference structure in the far field of the resonance cone

The interference structure of the resonance cone below the electron gyro-frequency (Whistler mode propagation) has been observed with electric and magnetic antennas in a large volume experimental magnetoplasma at distances greater than a wavelength from the transmitter.     

Effects of Spin Quantum Force in Magnetized Quantum Plasma

Starting from the governing equations for a quantum magnetoplasma including the electron spin -1/2 effects and quantum Bohm potential, we derive Korteweg-de Vries (KdV) equation of the system of quantum magnetohydrodynamics (QMHD). The amplitude and width of magnetosonic soliton with different parameters in the system are studied. It is found that the normalized Zeeman energy E plays a crucial role, for E≥1 the amplitude r_mξ and the width w_ξ of solitary wave all decrease as E increases. That is, the introduction of spin quantum force modifies the shape of solitary magnetosonic waves and makes them more narrower and shallower.     

Spin relaxation of two-dimensional electrons in a hall ferromagnet

Electron spin resonance in a system of two-dimensional electrons with a high electron mobility has been investigated and the position, width, intensity, and line shape of the resonance microwave absorption have been studied as functions of the filling factor and temperature. It has been shown that the ESR linewidth in high-electron-mobility GaAs/AlGaAs quantum wells may reach 30 MHz, which corresponds to a spin relaxation time of the two-dimensional electrons of 10 ns. The experimental data on the linewidth of the spin resonance at a filling factor of 1 are compared with the theoretical results for various spin relaxation mechanisms. It has been shown that the dominant mechanism of spin relaxation at a filling factor of 1 and a temperature of 1.5–4 K is the mutual scattering of spin excitons.     

Spin relaxation in GaAs/AlGaAs quantum wells in the vicinity of odd filling factors

Electron spin resonance in GaAs/AlGaAs quantum wells in the vicinity of odd filling factors ν = 3, 5, and 7 is investigated. The spin relaxation time of two-dimensional electrons is determined from the width of the microwave resonance absorption line. Dependences of the spin relaxation time on the filling factor, temperature, and orientation of the magnetic field are investigated. The spin relaxation time decreases noticeably upon deviation from odd filling factors, and its maximum value depends on the angle between the magnetic field and the plane of the two-dimensional electron gas.