Persistent current in metals with a large dephasing rate

Abstract

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...

Persistent currents in k-component Fibonacci mesoscopic rings threaded by a magnetic flux

“…All of these authors obtained the same order of magnitude for the PCs as those observed experimentally in [3]. More recently, with the development of fabrication techniques, more mesoscopic-scale experiments on PCs have been reported and introduced new challenges to the theoretical work, such as the sign of the PC near zero field and the correlation of the PC with the phase coherence time [6][7][8][9][10][11].…”

Magnetic Response of Disordered Metallic Rings: Large Contribution of Far Levels

“…Recently it was suggested that the largeness of the observed current is due to AC noise [21,22] or interactions of the electrons with two level systems [23], and a relation to dephasing was suggested (one should also keep in mind that the latter interactions may lead to an additional attractive interaction). We, however, consider T = 0, and do not include dephasing (we consider the dephasing length L φ to be larger than all relevant lengths).…”

Possible weak temperature dependence of electron dephasing

“…In particular, they do not enter the second-order calculation of defect-enhanced electron-electron interaction. 13 However, it will be shown that they play an important role in dephasing.…”