Quantum Hall effect in wide parabolic GaAs/<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Al</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">x</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ga</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mi mathvariant="normal">−</mml:m

Gwinn, E. G.; Westervelt, R. M.; Hopkins, P. F.; Rimberg, A. J.; Sundaram, M.; Gossard, A. C.

doi:10.1103/physrevb.39.6260

Cited by 90 publications

(26 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The same holds for the one-body density nHPT(r, t), and indeed for the entire many-body wave function, apart from the phase factor shown explicitly in (3). Note that the center of mass is tied to the accelerated (r) frame executing driven oscillator motion, and in this frame (3) is just the stationary state %0.…”

mentioning

confidence: 74%

See 1 more Smart Citation

Harmonic-Potential Theorem: Implications for Approximate Many-Body Theories

1994

View full text Add to dashboard Cite

We consider interacting particles in an external harmonic potential. We extend the 8 = 0 case of the generalized Kohn theorem, giving a "harmonic-potential theorem" (HPT), demonstrating rigid, arbitrary-amplitude, time-oscillatory Schrodinger transport of a many-body eigenfunction.We show analytically that the time-dependent local-density approximation (TDLDA) satisfies the HPT exactly. Other approximations, such as linearized TDLDA with frequency-dependent exchange correlation kernel and certain inhomogeneous hydrodynamic formalisms, do not. A simple modification permits such explicitly frequency-dependent local theories to satisfy the HPT, however. PACS numbers: 71.45.6m, 21.10.Re, 73.20.Dx, 73.20.Mf The Kohn theorem [1] concerns particles of mass m, and charge e with arbitrary momentum-conserving interactions plus a static external B field: It states that linear response to a uniform electric field Eo exp( -itot) yields a sharp resonance at to = co, = eB/mc, corresponding to cyclotron motion of the center of mass. Brey et al. [2] added an external scalar harmonic potential V,",(r) = Kz2/2 extending throughout all space. Their result (the "generalized Kohn theorem" or "GKT") also predicts sharp resonances for a uniform exciting field. In the electron-gas context, the static external harmonic potential can be generated, via Poisson s equation, by a uniform positive charge background extending throughout space, with charge density eno = aK/4n e, and this can be mimicked in GaA1As quantum wells, wires, and dots [2 -6]. (Here a is the background medium's relative dielectric constant. ) This paperconcerns only the case B = 0, for which the single GKT resonance frequency coo = (K/m*)'I2 is also equal to the plasma frequency at~= (4n. noe2/em*)'t~c orresponding to the fictitious background density no. The GKT resonance then corresponds to a "sloshing" or transverse plasmon motion of the electron gas.Note that the GKT does not apply to a charge-neutral electron gas as in a neutral metal slab of finite thickness: There the electron gas samples the nonparabolic linear region of external potential lying just outside the jellium edge [4].There is a fundamental difference between systems covered by the original Kohn theorem and those covered by the GKT: Unlike a B field, the harmonic scalar potential confines the density spatially so that, in the context of Coulomb-interacting systems, the GKT applies exactly to bounded, non-neutral electron gases with strong edge inhomogeneities [4]. The GKT is thus one of the few exact results known for the dynamic properties of an inhomogeneous, interacting many-particle system. We will show here that a slightly generalized GKT provides an interesting constraint on the general form of approximate theories of time-dependent phenomena in arbitrary inhomogeneous interacting systems. The GKT Hamiltonian for B = 0 with a spatially homogeneous time-dependent driving field E = F(t)/e-1S H(r~, r2, . . . , rtv t) = Ho -F(t) g.r, , H() = g=l h-'&al + -r) K. r, 2m (ar, ) 2 ' + V((r, -r, J). (2) Con...

show abstract

mentioning

confidence: 74%

“…Note that the center of mass is tied to the accelerated (r) frame executing driven oscillator motion, and in this frame (3) is just the stationary state %0. The phase factor in (3) transforms one back to the rest frame.…”

mentioning

confidence: 99%

Harmonic-Potential Theorem: Implications for Approximate Many-Body Theories

1994

View full text Add to dashboard Cite

show abstract

“…Addition of aluminium to the process leads to crystals of Gal~xAlxAs in which the aluminium fraction x can be controlled during growth. Thus x is a specified function x( z) of the position variable z measured in the crystal growth direction (Sundaram et al 1988;Gwinn et al 1989). Since the bandgap Eg and hence the conduction-band minimum Ec of this direct-gap semiconductor system depend on the aluminium fraction x, one can grow layered samples with a chosen spatial profile Ec (z).…”

Section: Introductionmentioning

confidence: 99%

Plasmons on Wide Epitaxially-grown Quantum Wells

Dobson¹

1993

Aust. J. Phys.

View full text Add to dashboard Cite

Aust. J. Phys., 1993, 46, 391~422 Quantum wells can now be grown by molecular beam epitaxy in the Gal~xAlxAs system with almost any desired electron confinement potential V (z) in the growth or z direction. The wells can be filled by remote doping, giving finely controllable high-mobility electron gases with a dimensionality between two and three. Grating coupler techniques permit observation at finite surface wavenumber of the infrared plasmon modes of these structures. This provides in principle a window onto fundamental and applicable many-electron physics. Of special interest are the 'pseudo-jellium' properties of parabolic and parabolic~linear wells, which are discussed in detail here. A theorem applicable to more general wells is also introduced.

show abstract

“…Much effort in fabricating, investigating and modelling wide quantum wells has been made in the past [1][2][3][4][5] According to the n-i-p-i concept, the design is based on a p-n-p structure with non-depleted n-and p-layers which form a wide quantum well (channel width 100-1000 nm) [6]. We use the compound semiconductor PbTe, grown on BaF 2 , as a host material [7].…”

Section: Introductionmentioning

confidence: 99%