Persistent Currents in Mesoscopic Connected Rings

Abstract

We report measurements of the low temperature magnetic response of a line of 16 GaAs/GaAlAs connected mesoscopic rings whose total length is much larger than l φ . Using an on-chip micro-squid technology, we have measured a periodic response, with period h/e, corresponding to persistent currents in the rings of typical amplitude 0.40 ± 0.08 nA per ring. Direct comparison with measurements on the same rings but isolated is presented.PACS numbers: 73.20.Dx, 72.20.My In a mesoscopic metallic sample, quantum coherence of the electronic wave functions can affect drastically the equilibrium properties of the system. In the case of a metallic ring in a magnetic field, the new boundary conditions imposed by the magnetic flux [1] lead the wave functions and therefore all the thermodynamic properties of the system to be periodic with flux, with periodicity Φ 0 = h/e, the flux quantum. One of the most striking consequences of this, first pointed out by Büttiker, Imry and Landauer [2] for the 1D case, is that a mesoscopic normal-metal ring pierced by a magnetic flux carries a persistent non-dissipative current: this is a consequence of the periodicity of the free energy F (Φ) with flux, implying the existence of an equilibrium current I(Φ) = −∂F (Φ)/∂Φ. Subsequently, much theoretical effort has been devoted to the description of a realistic 3D disordered ring [3][4][5][6][7]. Both the sign and the amplitude of this current depend on the number of electrons in the ring and on the microscopic disorder configuration: thus this current, like other mesoscopic phenomena such as Aharonov-Bohm conductance oscillations [8], is sample specific. However, the order of magnitude of the current for a single, isolated ring can be characterized by its typical value I typ = I 2 , denoting the average over disorder configurations. It is given [6,7] by I typ = 1.56 I 0 l e /L. In this formula, I 0 = ev F /L where v F is the Fermi velocity and L the perimeter of the ring, and l e is the elastic mean free path: the current varies as the inverse of the diffusion time τ D = L 2 /D where D = v F l e is the diffusion constant. When measuring an ensemble of rings, the typical current per ring decreases as 1/ √ N R , where N R is the number of rings. At finite temperature [6,7,9], mixing of the energy levels reduces the current on the scale of the Thouless energy E c , the energy scale for energy correlations. Further reduction arises when temperature reduces the phase coherence length l φ down to values lower than L.For a long time, persistent currents were believed to be a specific property of isolated systems [2]. However, recent theoretical predictions suggest that persistent currents should exist even in connected rings. Using a semi-classical model in the diffusive limit, ref.[10] calculated persistent currents in various networks of connected rings, showing that the amplitude of the persistent currents should be reduced only weakly as compared to its value in the same network of isolated rings, whereas all the other properties, like temper...

Electron kinetics in isolated mesoscopic rings driven out of equilibrium

“…Although an early theoretical study 8 of nonequilibrium conductivity in mesoscopic rings has predicted a peculiar effect of a direct current (DC), which is induced by an external alternating (ac) electromagnetic field, there has not been performed experimental search for this effect until very recently 6 .…”

“…Because of experimental difficulties, mesoscopic systems without leads have received less attention, except for a long-standing puzzle of persistent currents (PC) in normal metal rings in the Aharonov-Bohm configuration 1,2,3,4,5,6,7 . As the persistent current is an equilibrium mesoscopic phenomenon, most of theoretical papers deal with the thermodynamical properties of the electron system; it is assumed usually that the thermodynamic equilibrium has been sustained in the experimental investigations cited.…”

Spin-fluctuation-induced dephasing in a mesoscopic ring

“…Actually, a persistent current setup containing an external reservoir ͑without quantum dot͒ was realized in some previous experiments. 17,18 Our model is described by the Hamiltonianwhere H 0 , H R , and T stand for the hybrid dot-ring system, reservoir, and tunneling between the QD and reservoir, respectively. H 0 is decomposed into the three parts as…”

Pumping charge with ac magnetic fluxes and the dynamical breakdown of Onsager symmetry

“…In the absence of a dc driving voltage, these frequencies cast dc currents from 0.1 nA to a few nA. These currents are small but within the range observed in experiments on Aharanov-Bohm rings (see 3,[43][44][45][46].…”