Two-dimensional arrays of low capacitance tunnel junctions: general properties, phase transitions and Hall effect

We describe transport properties of two-dimensional arrays of low capacitance tunnel junctions, such as the current voltage characteristic and its dependence on external magnetic field and temperature. We discuss several experiments in which the small capacitance of the junctions plays an important role, and we also describe the methods for fabrication and measurements. In arrays where the junctions have a relatively large charging energy, (i.e. when they have a low capacitance) and a high normal state resistance, the low bias resistance increases with decreasing temperature and eventually at very low temperature the whole array may become insulating even though the electrodes in the array are superconducting. This transition to the insulating state can be described by thermal activation, characterized by an activation energy. We find that for certain junction parameters the activation energy oscillates with magnetic field with a period corresponding to one flux quantum per unit cell. In an intermediate region where the junction resistance is of the order of the quantum resistance and the charging energy is of the order of the Josephson coupling energy, the arrays can be tuned between a superconducting and an insulating state with a magnetic field. We describe measurements of this magnetic-field-tuned superconductor insulator transition, and we show that the resistance data can be scaled over several orders of magnitude. Four arrays follow the same universal functin provided we use a modified scaling parameter. We find a critical exponent close to unity, in good agreement with the theory. At the transition the transverse (Hall) resistance is found to be very small in comparison with the longitudinal resistance. However, for magnetic field values larger than the critical value. we observe a substantial Hall resistance. The Hall resistance of these arrays oscillates with the applied magnetic field. Features in the magnetic field dependence of the Hall resistance can qualitatively be correlated to features in the derivative of the longitudinal resistance, similar to what is found in the quantum Hall effect.