Persistent Currents in Mesoscopic Rings and Cylinders

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

doi:10.1103/physrevlett.62.587

Cited by 312 publications

(255 citation statements)

References 22 publications

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“…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 . For non-interacting electrons the grand canonical potential, and therefore the persistent current, depends only exponentially weak on the magnetic flux and one finds only a small persistent current [19].…”

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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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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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“…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.…”

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confidence: 99%

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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“…This is the so-called persistent current, an obvious demonstration of AB effect, and was first proposed by Büttiker et al 8 during early 80's. Following this pioneering work, substantial theoretical and experimental works [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] have been done along this line to understand different aspects of persistent current and other related issues in isolated conducting loops. In particular, the physics of quantum rings has always been the subject of intense research due to its potential applications in designing electronic, spintronic, optoelectronic and information processing devices.…”

Section: Introductionmentioning

confidence: 99%

“…These features are not discussed here as they are beyond the scope of our present work, and hopefully we will reproduce them in our forthcoming work. Now, the works involving flux-driven persistent current in isolated systems are mostly confined to simple loop geometries like single-channel rings, multi-channel cylinders, graphene rings, nanotubes, array of rings to name a few [9][10][11][12][13][14][15][16][17][18][19][20] . Whereas, very few works are available where twisted geometries have been taken into account.…”

Section: Introductionmentioning

confidence: 99%

Magnetic response of non-interacting and interacting electrons in a Möbius strip

Saha

Maiti

2016

Superlattices and Microstructures

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We investigate characteristic features of both non-interacting and interacting electrons in a Möbius strip, the simplest possible one-sided topological system, in presence of an Aharonov-Bohm flux φ. Using Hartree-Fock mean field theory we determine energy eigenvalues for the interacting model, while for the non-interacting system an analytical prescription is given. The interplay between longitudinal and vertical motions of electrons along with on-site Hubbard interaction yield several anomalous features of persistent current associated with energy-flux characteristics. The variation of current with system size and its temperature dependences are also critically examined. Current is highly sensitive to both these two factors, and we find that for a particular system size it decreases exponentially with temperature. Our analysis can be helpful in investigating electronic transport through any non-trivial topological material.

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Persistent Currents in Mesoscopic Rings and Cylinders

Cited by 312 publications

References 22 publications

Persistent current in metals with a large dephasing rate

Persistent current in metals with a large dephasing rate

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

Magnetic response of non-interacting and interacting electrons in a Möbius strip

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