Coulomb Drag in Mesoscopic Rings Typeset Using Revt E X

We develop a Luttinger liquid theory of the Coulomb drag of persistent currents flowing in concentric mesoscopic rings, by incorporating non-linear corrections to the electron dispersion relation. We demonstrate that at low temperatures, interactions between electrons in different rings generate an additional phase and thus alter the period of Aharonov-Bohm oscillations. We also show that interactions set a new temperature scale below which the linear response theory does not apply at certain values of external flux. 1 During the last decade, persistent currents (PC's) in mesoscopic rings have attracted significant interest both theoretically [1–6] and experimentally [7–9]. Much of this attention was due to a large discrepancy between experimentally observed current amplitudes in disordered metallic rings [7,8], and theoretical predictions based on a single-particle picture [2]. Yet unresolved, this puzzle has generated a number of theoretical works [3] on the role of electron-electron interactions in multi-channel disordered rings. At the same time, in clean single-channel rings the theory predicts that PC's at low temperatures should not be affected by interactions [10,4,6], and exhibit Aharonov-Bohm oscillations as a function of flux with the same period and amplitude as for non-interacting electrons. Results of a recent experiment on a single semiconductor ring with low number of channels are in agreement with these predictions [9]. On the other hand, interactions should become essential in a system consisting of a pair of clean 1D rings with different radii, placed concentrically, as is shown in Fig. 1. If the rings were isolated, PC's in each ring would oscillate with a period determined by its radius. Interring interactions will change the oscillation pattern by causing Coulomb drag of PC's, as we show below. There are, in general, two physical mechanisms for the current drag. The first mechanism [11], which originates from " friction " between two subsystems caused by scattering of carriers in one subsystem by density fluctuations in the other, has been widely studied during recent years [12], following experimental observation of the Coulomb drag [13]. At low temperatures, the resulting transresistance behaves as T 2 (T 2 ln T in a disordered system) and vanishes then with decreasing T as the phase space for scattering shrinks. The second, nondissipative mechanism was pointed out by Rojo and Mahan [14], and is based on the observation that the van der Waals interaction between two current carrying subsystems is modified, resulting in a finite current drag at …