Coherence and persistent currents in mesoscopic rings

Ambegaokar, Vinay; Eckern, Ulrich

doi:10.1103/physrevlett.65.381

Cited by 371 publications

(281 citation statements)

References 13 publications

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“…On the other hand, the effect of electron-electron interactions on the magnetic response is a much more controversial point. In particular, it has been invoked to be the necessary mechanism to obtain the measured values [77] for the problem of persistent currents in disorder metals. In a first approximation to the experimental conditions that we investigated in this work we would infer that electron-electron interactions are not crucial since the screening length is much smaller than the size of the samples and since the 2-d renormalization of the effective mass at these electron densities is only about 11% [78].…”

Section: Discussionmentioning

confidence: 99%

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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Section: Discussionmentioning

confidence: 99%

Orbital magnetism in the ballistic regime: geometrical effects

1996

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“…14 The electron-electron interaction in the presence of disorder is known to be of key importance in the physics of persistent currents in quantum rings. [15][16][17] Because SAQRs are strongly anisotropic, the potential acting on electrons is analogous to that in an axially symmetric ring with imperfections ͑see e.g., Ref. 5͒.…”

Section: Introductionmentioning

confidence: 99%

Energy spectra and oscillatory magnetization of two-electron self-assembledInxGa1−xAsquantum rings in GaAs

et al. 2008

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Citation for published version (APA):Fomin, V. M., Gladilin, V. N., Devreese, J. T., Kleemans, N. A. J. M., & Koenraad, P. M. (2008). Energy spectra and oscillatory magnetization of two-electron self-assembled Inx Ga1-x As quantum rings in GaAs. Physical Review B, 77(20) Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policy If you believe that this document breaches copyright please contact us at: openaccess@tue.nl providing details and we will investigate your claim. The effects of the Coulomb interaction on the energy spectrum and the magnetization of two electrons in a strained In x Ga 1−x As/ GaAs ringlike nanostructure are analyzed with realistic parameters inferred from the cross-sectional scanning-tunneling microscopy data. With an increasing magnetic field, the lowest spin-singlet and spin-triplet states sequentially replace each other as the ground state. This is reminiscent of the AharonovBohm effect for the ringlike structures. The exchange interaction leads to a more complicated oscillatory structure of the magnetic moment of the two electrons as a function of the magnetic field as compared to the magnetization pattern for a single-electron ringlike nanostructure. We discuss the relevance of the two-electron systems for the interpretation of the Aharonov-Bohm oscillations in the persistent current observed in low temperature magnetization measurements on self-assembled In x Ga 1−x As/ GaAs ringlike nanostructures.

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“…Except for the case of the nearly ballistic GaAs-AlGaAs ring [15], all the measured currents are in general one or two orders of magnitude larger than those expected from the theory [2,3,4,5,6,7,8,9,10,11,12]. The diamagnetic response of the measured φ 0 /2 oscillations of ensembleaveraged persistent currents near zero magnetic field also contrasts with most predictions [8,9].Free electron theory predicts that at T = 0, an or- * Corresponding author: Santanu K. Maiti E-mail: santanu@cmp.saha.ernet.in dered 1D metallic ring threaded by magnetic flux φ supports persistent current with maximum amplitude I 0 = ev F /L, where v F is the Fermi velocity and L is the circumference of the ring. Metals are intrinsically disordered which tends to decrease the persistent current, and the calculations show that the disorder-averaged current < I > crucially depends on the choice of the ensemble [3,4,5].…”

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confidence: 90%

Persistent currents with long-range hopping in 1D single-isolated-diffusive rings

2005

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We show from exact calculations that a simple tight-binding Hamiltonian with diagonal disorder and long-range hopping integrals, falling off as a power µ of the inter-site separation, correctly describes the experimentally observed amplitude (close to the value of an ordered ring) and flux-periodicity (hc/e) of persistent currents in single-isolated-diffusive normal metal rings of mesoscopic size. Long-range hopping integrals tend to delocalize the electrons even in the presence of disorder resulting orders of magnitude enhancement of persistent current relative to earlier predictions. Keywords: Model Calculations, MagnetotransportThe phenomenon of persistent current in mesoscopic normal metal rings has generated a lot of excitement as well as controversy over the past years. In a pioneering work, Büttiker, Imry and Landauer [1] predicted that, even in the presence of disorder, an isolated 1D metallic ring threaded by magnetic flux φ can support an equilibrium persistent current with periodicity φ 0 = ch/e, the flux quantum. Later, experimental observations confirm the existence of persistent currents in isolated mesoscopic rings. However, these experiments yield many results that are not well-understood theoretically even today [2,3,4,5,6,7,8,9,10,11,12,13]. The results of the single loop experiments are significantly different from those for the ensemble of isolated loops. Persistent currents with expected φ 0 periodicity have been observed in isolated single Au rings [14] and in a GaAs-AlGaAs ring [15]. Levy et al. [16] found oscillations with period φ 0 /2 rather than φ 0 in an ensemble of 10 7 independent Cu rings. Similar φ 0 /2 oscillations were also reported for an ensemble of disconnected 10 5 Ag rings [17] as well as for an array of 10 5 isolated GaAs-AlGaAs rings [18]. In a recent experiment, Jariwala et al.[19] obtained both φ 0 and φ 0 /2 periodic persistent currents in an array of thirty diffusive mesoscopic Au rings. Except for the case of the nearly ballistic GaAs-AlGaAs ring [15], all the measured currents are in general one or two orders of magnitude larger than those expected from the theory [2,3,4,5,6,7,8,9,10,11,12]. The diamagnetic response of the measured φ 0 /2 oscillations of ensembleaveraged persistent currents near zero magnetic field also contrasts with most predictions [8,9].Free electron theory predicts that at T = 0, an or- * Corresponding author: Santanu K. Maiti E-mail: santanu@cmp.saha.ernet.in dered 1D metallic ring threaded by magnetic flux φ supports persistent current with maximum amplitude I 0 = ev F /L, where v F is the Fermi velocity and L is the circumference of the ring. Metals are intrinsically disordered which tends to decrease the persistent current, and the calculations show that the disorder-averaged current < I > crucially depends on the choice of the ensemble [3,4,5]. The magnitude of the current < I 2 > 1/2 is however insensitive to the averaging issues, and is of the order of I 0 l/L, l being the elastic mean free path of the electrons. This expression...

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Coherence and persistent currents in mesoscopic rings

Cited by 371 publications

References 13 publications

Orbital magnetism in the ballistic regime: geometrical effects

Orbital magnetism in the ballistic regime: geometrical effects

Energy spectra and oscillatory magnetization of two-electron self-assembledInxGa1−xAsquantum rings in GaAs

Persistent currents with long-range hopping in 1D single-isolated-diffusive rings

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