Average persistent current in a mesoscopic ring

Oppen, Felix von; Riedel, Eberhard K.

doi:10.1103/physrevlett.66.84

Cited by 265 publications

(135 citation statements)

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“…[1,4]. Theory, when neglecting electron interactions, predicts a current that is of the order I ∼ eδ/h, where δ is the average distance of single particle levels at the Fermi energy [5][6][7]. With the parameters of the experiment [3], δ/k ≈ 0.2mK and E c /k ≈ 25mK, the current obtained is about two orders of magnitude too small.…”

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confidence: 99%

“…For simplicity we do not discuss the subtle questions concerning differences between the canonical F (N, φ) and the grand canonical thermodynamical potential Ω(µ, φ) [5][6][7]. In an ensemble of weakly disordered rings the disorder configuration will change from ring to ring, so in order to calculate the average persistent current of an ensemble of rings one has to average over disorder, I(φ) → I(φ) dis .…”

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confidence: 99%

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Persistent current in metals with a large dephasing rate

Schwab

2000

Eur. Phys. J. B

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In a weakly disordered metal electron interactions are responsible for both decoherence of the quasi-particles as well as for quantum corrections to thermodynamic properties. We consider electrons which are interacting with two-level-systems. We show that the two-level-systems enhance the average equilibrium ("persistent") current in an ensemble of mesoscopic rings. The result supports the recent suggestion that two puzzles in mesoscopic physics may be related: The low temperature saturation of the dephasing time and the high persistent current in rings.PACS numbers: 05.30Fk, 73.23.RaQuantum interference effects play a crucial role in the low temperature properties of normal metals. Prominent examples are weak localization and the associated magnetoresistance. Recently it was suggested [1,2] that two of the unresolved problems in the physics of mesoscopic metals may have a common solution: The large value of the persistent current in mesoscopic rings and the low temperature saturation of the dephasing rate which is seen in magnetoresistance measurements.The first problem is the large value of the persistent current in rings. Lévy et al [3] measured the nonlinear response to a magnetic field of an ensemble of 10 7 mesoscopic copper rings. The measured signal corresponds to a current I ≈ I 0 sin(2πφ/φ 0 ) circulating in each ring. φ is the magnetic flux which penetrates each ring and φ 0 = h/e is the flux quantum. For temperatures in the mK regime the amplitude was |I 0 | ≈ 0.3nA per ring, which is of the order of one elementary charge in the time τ D an electron needs to diffuse around the ring,is the Thouless energy, D is the electron diffusion constant, and L is the circumference of the ring. Similar results were reported in Refs. [1,4]. Theory, when neglecting electron interactions, predicts a current that is of the order I ∼ eδ/h, where δ is the average distance of single particle levels at the Fermi energy [5][6][7]. With the parameters of the experiment [3], δ/k ≈ 0.2mK and E c /k ≈ 25mK, the current obtained is about two orders of magnitude too small. Electron interactions first seemed to improve the situation [8]. For Coulomb interaction it was found that I ∼ eµ * E c /h, where µ * is a dimensionless number that characterizes the strength of the interaction in the Cooper channel. However estimates of µ * gave a value which is an order of magnitude too small when comparing it with the experiment [8]. Surprisingly an enhancement of the current was also reported in presence of a moderate concentration of magnetic impurities [9], with I ∼ e(E c /h)·min(h/τ s , E c )/kT , where 1/τ s is the spin-flip scattering rate. This can become larger than the current coming from the Coulomb interaction, however since the temperature dependence is different from the one observed this mechanism has not been considered as a possible explanation of the experiment in Ref. [3].The second problem concerns the phase coherence of the electrons. Whereas it is expected that the dephasing rate goes to zero in the zero temperature li...

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confidence: 99%

Persistent current in metals with a large dephasing rate

Schwab

2000

Eur. Phys. J. B

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“…For a single ring this current is expected to oscillate with a period φ 0 [20], and this prediction has been confirmed in two experiments [21,22]. Upon ensemble-averaging with a fixed particle number, the periodicity is expected to change to φ 0 /2 [23,24,25], in agreement with several observations on systems with a large number of disconnected rings [26,27,28]. Ensemble-averaging with a fixed chemical potential instead of a fixed particle-number preserves a dominant φ 0 periodicity [29].…”

Section: Rg Resultsmentioning

confidence: 88%

Strong-disorder renormalization-group method on fractal lattices: Heisenberg models and magnetoresistive effects in tight-binding models

2005

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We use a numerical implementation of the strong disorder renormalization group (RG) method to study the low-energy fixed points of random Heisenberg and tight-binding models on different types of fractal lattices. For the Heisenberg model new types of infinite disorder and strong disorder fixed points are found. For the tight-binding model we add an orbital magnetic field and use both diagonal and off-diagonal disorder. For this model besides the gap spectra we study also the fraction of frozen sites, the correlation function, the persistent current and the two-terminal current. The lattices with an even number of sites around each elementary plaquette show a dominant φ0 = h/e periodicity. The lattices with an odd number of sites around each elementary plaquette show a dominant φ0/2 periodicity at vanishing diagonal disorder, with a positive weak localization-like magnetoconductance at infinite disorder fixed points. The magnetoconductance with both diagonal and off-diagonal disorder depends on the symmetry of the distribution of on-site energies.

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“…The explanation presented above for the φ0 2 -periodicity of I(φ) is connected with the transition from the grand canonical ensemble averaging to the canonical one [8,11,12,17,18,30]. Another consideration also seems to be pertinent.…”

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confidence: 99%

“…However, the coherent backscattering mechanism with consequent interference effects in mesoscopic systems gives rise to conductance oscillations with the halved period φ 0 /2 [1, [11][12][13][14][15]. It is pertinent to notice that the attempt to explain the φ 0 /2 oscillation in a disordered ring by taking into account the electron-electron interaction [15][16][17][18][19] is also based on the "cooperon" propagation in the system. All these disputes in the theory seem to be connected with the absence of a consistent theory for a one-dimensional (1d) disordered ring in a magnetic field which goes beyond the diffusion approximation and can calculate not only average values of the physical parameters but also mesoscopic fluctuations of these parameters.…”

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confidence: 99%

Aharonov-Bohm effect in one-channel weakly disordered rings

2000

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A new diagrammatic method, which is a reformulation of Berezinskii's technique, is constructed to study the density of electronic states ρ(ǫ, φ) of a one-channel weakly disordered ring, threaded by an external magnetic flux. The exact result obtained for the density of states shows an oscillation of ρ(ǫ, φ) with a period of the flux quantum φ0 = hc e . As the sample length (or the impurity concentration) is reduced, a transition takes place from the weak localization regime (L ≫ l) to the ballistic one (L ≤ l). The analytical expression for the density of states shows the exact dependence of ρ(ǫ, φ) on the ring's circumference and on disorder strength for both regimes. 71.10.-w, 71.20.-b, 71.55.i, 73.23.-b The oscillation of physical properties of disordered metals has been studied intensively after the prediction of the Aharonov-Bohm effect in doubly connected dirty systems [1] with the period of half of a flux quantum and its observation [2] in a Mg cylinder.Today, a particular subject of intensive investigation is the persistent current, predicted in [3,4] for one-dimensional disordered rings. Recent advances in microstructure technology facilitate the fabrication of mesoscopic rings and the observation of thermodynamic currents therein [5][6][7]. The observed oscillatory responses in these experiments, which are consistent with a persistent current, differ in the period of oscillation.A similar controversy exists also in theory. According to fundamental physical principles all physical parameters, in particular the persistent current, of a one-channel metal ring should be periodic in an applied magnetic flux φ with period of a flux quantum φ 0 = hc e [3,4,[8][9][10]. However, the coherent backscattering mechanism with consequent interference effects in mesoscopic systems gives rise to conductance oscillations with the halved period φ 0 /2 [1, [11][12][13][14][15]. It is pertinent to notice that the attempt to explain the φ 0 /2 oscillation in a disordered ring by taking into account the electron-electron interaction [15][16][17][18][19] is also based on the "cooperon" propagation in the system. All these disputes in the theory seem to be connected with the absence of a consistent theory for a one-dimensional (1d) disordered ring in a magnetic field which goes beyond the diffusion approximation and can calculate not only average values of the physical parameters but also mesoscopic fluctuations of these parameters.It is well known that the physical parameters of a mesoscopic system with dimension L satisfying the condition l < L ≪ l in (where l is the mean free path and l in is the length over which the phase coherence of an electron wave is conserved) have random character, i.e. self-averaging is violated [20]. At T = 0 all systems become mesoscopic. In this case high moments give a considerable contribution, which results in strong differences between average value and typical one of the observed parameter [21], i.e. the average value loses its significance to characterize the experimental observation. F...

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Average persistent current in a mesoscopic ring

Cited by 265 publications

References 14 publications

Persistent current in metals with a large dephasing rate

Persistent current in metals with a large dephasing rate

Strong-disorder renormalization-group method on fractal lattices: Heisenberg models and magnetoresistive effects in tight-binding models

Aharonov-Bohm effect in one-channel weakly disordered rings

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