Persistent currents in finite-width mesoscopic rings

Groshev, A. G.; Kostadinov, I.Z.; Dobrianov, I.

doi:10.1103/physrevb.45.6279

Cited by 9 publications

(11 citation statements)

References 11 publications

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“…Recently, the electronic properties of low-dimensional structures with a ring geometry have been extensively studied including Aharonov-Bohm ͑AB͒ effects, 1-9 persistent currents, [12][13][14][15][16][17][18][19][20] and quantum chaos. 13 The original picture of both the AB effect and the persistent current in a ring geometry is very simple: Considering a one-dimensional ͑1D͒ ring pierced by an AB magnetic flux ͑i.e., an infinitely thin flux tube͒ confined to its center, the magnetic flux has a purely gauge effect.…”

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confidence: 99%

Landau quantization and the Aharonov-Bohm effect in a two-dimensional ring

1996

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We propose an exactly soluble model for a ring with finite width. Exact energy spectra and wave functions are obtained analytically for a ring in the presence of both a uniform perpendicular magnetic field and a thin magnetic flux through the ring center. We use the model to study the Aharonov-Bohm ͑AB͒ effect in an ideal annular ring that is weakly coupled to both the emitter and the collector. It is found that, for such a weakly coupled ring in a uniform magnetic field, not only do the electron states in different subbands of the ring produce different AB frequencies, the clockwise and anticlockwise moving states in the same subband also lead to two different AB frequencies. Therefore, when many subbands in the ring are populated, the large number of different AB frequencies generally result in an aperiodic AB oscillation. More striking is that, even when only one subband is populated, the two AB frequencies corresponding to the states moving in opposite directions also cause beating in the AB oscillations. We have obtained explicit expressions for all these AB frequencies. Our results produce a clear explanation for the recent experimental observation of Liu and coworkers.

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confidence: 99%

Landau quantization and the Aharonov-Bohm effect in a two-dimensional ring

1996

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“…So far, no use has been made of the complexity of the de Gennes distances: Eqs. (26), (29) -(36) are valid for either real or complex parameters Λ. Miscellaneous cases of the real Robin parameter and different combinations of the background B and the AB fields for the same 2D geometry have been addressed before [15,24,48,52,53,84,85,[89][90][91][92][93][94][95][96] in the framework of the formalism of linear equations (2) or (9); in particular, Eq. (35) for the Dirichlet boundary conditions was presented in [84,85,89] with its uniform magnetic counterpart for zero AB flux given in [92,94] while Eq.…”

Section: Model and Formulationmentioning

confidence: 99%

Guiding structures with multiply connected cross sections: Evolution of propagation in external fields at complex Robin parameters

Olendski¹

2012

Annals of Physics

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Properties of the two-dimensional ring and three-dimensional infinitely long straight hollow waveguide with unit width and inner radius ρ0 in the superposition of the longitudinal uniform magnetic field B and Aharonov-Bohm flux are analyzed within the framework of the scalar Helmholtz equation under the assumption that the Robin boundary conditions at the inner and outer confining walls contain extrapolation lengths Λin and Λout, respectively, with nonzero imaginary parts. It is shown that, compared to the disk geometry, the annulus opens up additional possibilities of varying magnetization and currents by tuning imaginary components of the Robin parameters on each confining circumference; in particular, the possibility of restoring a lossless longitudinal flux by zeroing imaginary part Ei of the total transverse energy E is discussed. The energy E turns real under special correlation between the imaginary parts of Λin and Λout with the opposite signs what corresponds to the equal transverse fluxes through the inner and outer interfaces of the annulus. In the asymptotic case of the very large radius, simple expressions are derived and applied to the analysis of the dependence of the real energy E on Λin and Λout. New features also emerge in the magnetic field influence; for example, if, for the quantum disk, the imaginary energy Ei is quenched by the strong intensities B, then for the annulus this takes place only when the inner Robin distance Λin is real; otherwise, it almost quadratically depends on B with the corresponding enhancement of the reactive scattering. Closely related problem of the hole in the otherwise uniform medium is also addressed for real and complex extrapolation lengths with the emphasis on the comparative analysis with its dot counterpart.

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“…Of particular interest quantum phenomena of electrons in mesoscopic rings including Aharonov-Bohm (AB) effects, 1-9 persistent currents, [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] and quantum chaos 11 have been investigated extensively both theoretically and experimentally. The physical origin of the appearance of the persistent current induced in a one-dimensional (ID) mesoscopic ring by an AB magnetic flux was well understood.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, analyses of persistent currents in an annulus with a finite width were carried out a few years ago. [15][16][17][18][19] More recent, the importance of many channel effects owing to the finite width of the annulus has been addressed and several authors considered twodimensional (2D) and 3D cylindrical rings threaded by a flux along the axis. 17 " 19 Significant theoretical effects have been devoted to the study of the finite-width effect on AB oscillations 6 " 9 and persistent currents.…”

Section: Introductionmentioning

confidence: 99%

“…17 " 19 Significant theoretical effects have been devoted to the study of the finite-width effect on AB oscillations 6 " 9 and persistent currents. [15][16][17][18][19][20][21][22][23][24][25][26][27][28] In this article we investigate the characteristics of the persistent currents in an annular ring with one radial potential barrier inside it, threading magnetic flux through its hole. In the previous work, 29 we have studied the similar structures under the application of uniform magnetic fields in the annular area.…”

Section: Introductionmentioning

confidence: 99%

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Energy Spectrum and Persistent Currents in Finite-Width Mesoscopic Ring with Radial Potential Barrier Threading a Magnetic Flux Through its Hole

Sheng

Wang

1998

Int. J. Mod. Phys. B

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The energy spectrum and the persistent currents are calculated for a finite-width mesoscopic annulus with radial potential barrier, threading a magnetic flux through the hole of the ring. Owing to the presence of tunneling barrier, the coupling effect leads to the splitting of each radial energy subband of individual concentrical rings into two one. Thus, total currents and currents carried by single high-lying eigenstate as a function of magnetic flux exhibit complicated patterns. However, periodicity and antisymmetry of current curves in the flux still preserve.

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Persistent currents in finite-width mesoscopic rings

Cited by 9 publications

References 11 publications

Landau quantization and the Aharonov-Bohm effect in a two-dimensional ring

Landau quantization and the Aharonov-Bohm effect in a two-dimensional ring

Guiding structures with multiply connected cross sections: Evolution of propagation in external fields at complex Robin parameters

Energy Spectrum and Persistent Currents in Finite-Width Mesoscopic Ring with Radial Potential Barrier Threading a Magnetic Flux Through its Hole

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