Classical continuum theory of the dipole-forbidden collective excitations in quantum strips

Wl, Schaich; Mr, Geller; Vignale, Giovanni

doi:10.1103/physrevb.53.13016

Cited by 5 publications

(4 citation statements)

References 36 publications

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“…The strip is oriented along the z axis, and we assume the density to be uniform in this direction. The collective modes in this system have been studied 14,19 using a classical approach ͑which does not include damping͒, and we here briefly summarize the results. The classical equation of motion for the velocity field u(y,t) of the 2D electron fluid ͑without external driving field͒ reads…”

Section: A Solution Of the Linearized Classical Equation Of Motionmentioning

confidence: 99%

“…IV to collective modes in twodimensional ͑2D͒ quantum strips. 14 The advantage of these systems is that they can be treated analytically, within a hydrodynamical approximation, and thus allow us to gain systematic insight into the damping of collective modes in an inhomogeneous model system. We find that the boundary effects caused by the confinement of the 2D electron gas ͑2DEG͒ lead to a strong enhancement of the linewidth as compared to the homogeneous case.…”

Section: Introductionmentioning

confidence: 99%

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Linewidths of collective excitations of the inhomogeneous electron gas: Application to two-dimensional quantum strips

Ullrich

Vignale

1998

Phys. Rev. B

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It is well known that high-frequency collective excitations in electronic systems are not Landau damped, i.e., they cannot decay effectively into single particle-hole pairs. The leading damping mechanism in this regime is instead provided by dynamical exchange and correlation effects, such as multipair production. These effects are not captured by the widely used adiabatic local-density approximation ͑ALDA͒, which accounts for Landau damping only. In the recently developed time-dependent current density-functional formalism ͓G. Vignale, C. A. Ullrich, and S. Conti, Phys. Rev. Lett. 79, 4878 ͑1997͔͒, exchange and correlation enter as viscoelastic stresses in the electron fluid, causing an additional damping that is not contained in the ALDA. We use this theory to derive an explicit formula for the linewidth of collective electronic excitations that are not Landau damped. The formula is then applied to calculate the linewidth of collective modes in two-dimensional ͑2D͒ quantum strips. In comparison with the corresponding modes in the homogeneous 2D electron gas, we find an order-of-magnitude enhancement of the linewidth due to the nonuniformity of the system.

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Section: A Solution Of the Linearized Classical Equation Of Motionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Linewidths of collective excitations of the inhomogeneous electron gas: Application to two-dimensional quantum strips

Ullrich

Vignale

1998

Phys. Rev. B

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“…Recent experimental results concern parabolic or near-parabolic confinement potentials 2 for which the so-called harmonicpotential theorem (HPT) states that an external dipole excitation can only couple to a rigid-shift mode (Kohn mode 6 ) at frequency K/m * independently of the excitation strength 7 (m * is the effective electron mass and K the curvature of v 0 ). In its original formulation, the HPT is a quantum-mechanical theorem 7,8 ; it was shown 9 to hold in classical mechanics also.…”

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Optical Response of Two-Dimensional Electron Fluids Beyond the Kohn Regime: Strong Nonparabolic Confinement and Intense Laser Light

2002

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We investigate the linear and nonlinear optical response of two-dimensional interacting electron fluids confined by a strong nonparabolic potential. We show that such fluids may exhibit higher-harmonic spectra under realistic experimental conditions. Higher harmonics arise as the electrons explore anharmonicities of the confinement potential (electron-electron interactions reduce this nonlinear effect). This opens the possibility of controlling the optical functionality by engineering the confinement potential. Our results were obtained within time-dependent density-functional theory. A classical hydrodynamical model is in good agreement with the quantum-mechanical results.

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“…As for narrow quantum strips with parabolic confining potentials, Schaich et al have analyzed dipole-forbidden collective excitations in the conduction-electron system, 17 and Ullrich and Vignale have examined dynamical XC effects on damping of collective excitations. 18 A finite domain of the )ϫ)-Ag structure newly realizes an ideal 2D conduction-electron system confined in a finite region.…”

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Characteristics of low-dimensional plasmons in a metallic strip monolayer on a semiconductor surface

Inaoka

2003

Phys. Rev. B

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By means of the time-dependent local-density approximation, we investigate low-dimensional plasmons ͑LDPL's͒ in a metallic strip monolayer on a semiconductor surface, namely, LDPL's in a two-dimensional conduction-electron system confined in a strip region. We analyze the energy-loss intensity, the energy dispersion, and the induced-charge distribution of the two plasmon modes at each wave number q along the strip. When the wavelength (ϭ2/q) of the mode is considerably smaller than the strip width D, the higherenergy mode ͑HEM͒ has a definite character of the area plasmon ͑APL͒, and its energy is close to that of the two-dimensional plasmon in an infinite area ͑pure 2DPL͒. However, as the mode energy deviates upward from that of the pure 2DPL with an increase in , the induced-charge distribution of the APL evolves into a standing-wave pattern with its free end at the edge. In contrast, the lower-energy mode ͑LEM͒ has a definite character of the edge plasmon. When is small compared with D, the induced charge density of the LEM decays slowly on the inside of the strip owing to the influence of the HEM ͑APL͒ close to the LEM in energy. The Si (111)-)ϫ)-Ag surface can be formed by depositing one monolayer of Ag atoms on a Si (111)-7ϫ7 surface at temperatures higher than 250°C.1-3 One of the three surface-state bands known, namely, the S 1 -state band provides an ideal two-dimensional ͑2D͒ system of conduction electrons. The electron density in this band varies among experiments, 4 -6 because it significantly depends upon presence of a minute amount of extra Ag adatoms 4 -6 or other possible dopant impurities or surface states.The conduction-electron character of the S 1 states can be visualized in low-temperature scanning-tunnelingmicroscopy ͑STM͒ images from a )ϫ)-Ag domain surrounded by atomic steps or out-of-phase ͑OP͒ boundaries. 2,7One can observe those standing waves which originate from interference of electronic waves impinging on and reflected from the steps or boundaries. Near the step or the OP boundary, we clearly notice corrugation patterns due to this interference with intervals of a few tens of Å, even if the ) ϫ)-Ag structure is established on both sides of the step or boundary.7 This indicates that the S 1 electrons are confined in each )ϫ)-Ag domain by a potential barrier at the step or boundary. The domain can have various shapes, such as a circular one, a squarelike one, and a strip extending on a terrace. 2,7Quite recently, by means of high-resolution electron energy-loss spectroscopy ͑HREELS͒, Nagao et al. have clearly observed two-dimensional plasmons ͑2DPL's͒ due to the S 1 -state band that occur in a virtually infinite area.8 Taking account of exchange-correlation ͑XC͒ effects, Inaoka et al. have investigated the energy dispersion and the energyloss intensity of the 2DPL in relation to the above experiment. 9In a bounded 2D electron system occur edge plasmons ͑EPL's͒ localized near the edge and area plasmons ͑APL's͒ extending widely on the inside. Especially, studies of the EPL's can be trac...

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Classical continuum theory of the dipole-forbidden collective excitations in quantum strips

Cited by 5 publications

References 36 publications

Linewidths of collective excitations of the inhomogeneous electron gas: Application to two-dimensional quantum strips

Linewidths of collective excitations of the inhomogeneous electron gas: Application to two-dimensional quantum strips

Optical Response of Two-Dimensional Electron Fluids Beyond the Kohn Regime: Strong Nonparabolic Confinement and Intense Laser Light

Characteristics of low-dimensional plasmons in a metallic strip monolayer on a semiconductor surface

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