Quantum phase transitions in capacitively coupled two-dimensional Josephson-junction arrays

Quantum phase transitions in two layers of ultrasmall Josephson junctions, coupled capacitively with each other, are investigated. As the inter-layer capacitance is increased, the system at zero temperature is found to exhibit an insulator-to-superconductor transition. It is shown that, unlike in the case for one-dimensional arrays with a similar coupling configuration, the transition cannot be accounted for exclusively by particle–hole pairs. Capacitively coupled systems of charges have attracted significant attention in recent years, raising the possibility of current drag effects: the current fed through either of the systems, owing to Coulomb interaction, induces a secondary current in the other system. Such a drag effect depends strongly on the dimensionality and the structure of the system as regards its mechanism and behaviour. The current drag in two capacitively coupled twodimensional (2D) electron gases [1] was attributed to a momentum-transfer mechanism due to Coulomb scattering [2] and is fairly small in magnitude. By contrast, recent theoretical predictions [3] and experimental demonstrations [4, 5] with two capacitively coupled onedimensional (1D) arrays of submicron metallic tunnel junctions have shown that the primary and the secondary currents are comparable in magnitude but opposite in direction in a certain region of applied voltage. In such tunnel junction systems, the current drag is attributed to the transport of electron–hole pairs, which are bound by the electrostatic energy of the coupling capacitance. Lately, it has been suggested that the momentum-transfer mechanism can also lead to absolute current drag in 1D electron channels coupled electrostatically with each other [6]. The current drag effects in capacitively coupled 2D arrays of tunnel junctions have not been studied and will be examined in this work. More interestingly, when the tunnelling junctions are composed of ultrasmall superconducting grains, the counterpart of the electron–hole pair becomes the pair of excess and deficit Cooper pair, which will simply be called the particle–hole pair. Furthermore, in such ultrasmall Josephson-junction systems the competition between the charging energy and the Josephson coupling energy is well known to lead to novel effects of quantum fluctuations [7–10]. Combined with these quantum fluctuation effects, the pair transport phenomena in coupled 1D Josephson-junction arrays (JJAs) have recently been proposed to drive an insulator-to-superconductor transition [11]. In this paper, two 2D arrays of ultrasmall Josephson junctions, coupled capacitively with each other, are considered. Quantum phase transitions are examined at zero temperature, † Present address: Centre for Theoretical Physics, Seoul National University, Seoul 151-742, Korea. 0953-8984/98/439783+07$19.50 c © 1998 IOP Publishing Ltd 9783