Experimental investigation of two-dimensional arrays of ultrasmall Josephson junctions

We have measured Current-Voltage ( I-V ) characteristics of a large number of two-dimensional arrays of small area Al-AlOx-Al junctions down to temperatures of 40 mK, recording the temperature dependence of the zero bias resistance R 0 ( T ). The normal state resistance of the junctions R N varies from 2 kΩ to 270 kΩ and the junction capacitance C from 0.2 f F to 2.2 f F. The arrays are classified into different types according to the E J / E c and the R Q / R N ratios, and mapped onto a parameter diagram. E J is the Josephson coupling energy, E c = e 2 /2 C is the charging energy, and R Q = h /4 e 2 = 6.5 kΩ is the quantum resistance. For low resistance arrays, R Q / R N >> 1 with E J / E c > 1, the Josephson current prevails and the arrays are superconducting. When R Q / R N << 1 and E J / E c < 1, the I-V characteristics show typical Coulomb blockade features. In an intermediate region where R Q / R N similar 0.4, E J / E c similar 0.2, we find a "back-bending" I-V curve with negative differential resistance. The behavior of R 0 ( T ) also falls into three categories which can be correlated with the type of I-V characteristic. At the lowest temperature the arrays appear to be either insulating (d R 0 /d T < 0) or superconducting (d R 0 /d T > 0) depending on whether R N is greater than R Q or less than R Q respectively.