Isolated rings of mesoscopic dimensions. Quantum coherence and persistent currents

Cheung, Ho-Fai; Gefen, Yuval; Riedel, Eberhard K.

doi:10.1147/rd.323.0359

Cited by 139 publications

(133 citation statements)

References 16 publications

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“…(4.39) and Ref. [32] would yield 7nA. The difference between the theoretical and measured values is not significant given the experimental uncertainties as discussed in Refs.…”

Section: Comparison With Experimentsmentioning

confidence: 72%

“…[32]. For the next order term the contribution from type-I trajectories is cancelled by that of type-II resulting in the relatively flat character of the curves for I (t) in Fig.…”

Section: Thin Ringsmentioning

confidence: 92%

“…These latter studies started usually from very general considerations without making the connection with the Landau diamagnetism. The pioneering work of Büttiker, Imry and Landauer [29] demonstrating that in the presence of magnetic flux the ground state of a one dimensional ring has a current flow generated a large theoretical activity, mainly directed towards generalizations of quasi-one dimensional and diffusive rings [30,32]. The first experimental evidence of persistent currents in an ensemble of mesoscopic copper rings was given by the 1990 measurement of Lévy et al [33].…”

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confidence: 99%

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Orbital magnetism in the ballistic regime: geometrical effects

1996

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We present a general semiclassical theory of the orbital magnetic response of noninteracting electrons confined in two-dimensional potentials. We calculate the magnetic susceptibility of singly-connected and the persistent currents of multiply-connected geometries. We concentrate on the geometric effects by studying confinement by perfect (disorder free) potentials stressing the importance of the underlying classical dynamics. We demonstrate that in a constrained geometry the standard Landau diamagnetic response is always present, but is dominated by finite-size corrections of a quasi-random sign which may be orders of magnitude larger. These corrections are very sensitive to the nature of the classical dynamics. Systems which are integrable at zero magnetic field exhibit larger magnetic response than those which are chaotic. This difference arises from the large oscillations of the density of states in integrable systems due to the existence of families of periodic orbits. The connection between quantum and classical behavior naturally arises from the use of semiclassical expansions. This key tool becomes particularly simple and insightful at finite temperature, where only short classical trajectories need to be kept in the expansion. In addition to the general theory for integrable systems, we analyze in detail a few typical examples of experimental relevance: circles, rings and square billiards. In the latter, extensive numerical calculations are used as a check for the success of the semiclassical analysis. We study the weak-field regime where classical trajectories remain essentially unaffected, the intermediate field regime where we identify new oscillations characteristic for ballistic mesoscopic structures, and the high-field regime where the typical de Haas-van Alphen oscillations exhibit finite-size corrections. We address the comparison with experimental data obtained in high-mobility semiconductor microstructures discussing the differences between individual and ensemble measurements, and the applicability of the present model. 03.65.Sq,05.45.+b,05.30.Fk,73.20.Dx

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“…(4.39) and Ref. [32] would yield 7nA. The difference between the theoretical and measured values is not significant given the experimental uncertainties as discussed in Refs.…”

Section: Comparison With Experimentsmentioning

confidence: 72%

“…[32]. For the next order term the contribution from type-I trajectories is cancelled by that of type-II resulting in the relatively flat character of the curves for I (t) in Fig.…”

Section: Thin Ringsmentioning

confidence: 92%

mentioning

confidence: 99%

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Orbital magnetism in the ballistic regime: geometrical effects

1996

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“…This parameter can be chosen to be exp(−d/d φ ) as in Ref. 31, wherein d is as defined above while d φ is the phase coherence length. This phase coherence length can be expressed in terms of the dephasing time (τ φ ), as d φ = v f τ φ wherein v f is the Fermi velocity of electrons traversing the system.…”

Section: Inelastic Scatteringmentioning

confidence: 99%

Quantum spin pumping with adiabatically modulated magnetic barriers

Benjamin

2004

Phys. Rev. B

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A quantum pump device involving magnetic barriers produced by the deposition of ferro magnetic stripes on hetero-structures is investigated. The device for dc-transport does not provide spinpolarized currents, but in the adiabatic regime, when one modulates two independent parameters of this device, spin-up and spin-down electrons are driven in opposite directions, with the net result being that a finite net spin current is transported with negligible charge current. We also analyze our proposed device for inelastic-scattering and spin-orbit scattering. Strong spin-orbit scattering and more so inelastic scattering have a somewhat detrimental effect on spin/charge ratio especially in the strong pumping regime. Further we show our pump to be almost noiseless, implying an optimal quantum spin pump.

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“…The first theoretical works on persistent currents have been in one-dimensional ͑1D͒ ring geometries, 6 in two-dimensional ͑2D͒ the computations have been performed employing discrete models or cylindrical geometries. 7,8 In the last case, the mathematical description of the problem is essentially the same as for the ring geometries because the eigenenergies are pure quadratic forms of the two quantum numbers with a functional dependence on the flux that is identical to 1D systems.…”

Section: Towards An Analytical Formula For the Eigenvalues Of The Ahamentioning

confidence: 99%