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Physical Review Letters

Charging effects and quantum coherence in regular Josephson junction arrays

Lambert J. Geerligs, M. Peters, L. E. M. de Groot, A. H. Verbruggen, Johan E. Mooij

Published Jul 17, 1989• 242 citations
Publisher

Abstract

Two-dimensional arrays of very-small-capacitance Josephson junctions have been studied. At low temperatures the arrays show a transition from superconducting to insulating behavior when the ratio of charging energy to Josephson-coupling energy exceeds the value 1. Insulating behavior coincides withthe occurrence of a charging gap inside the BCS gap, with an S-shaped I-V characteristic. This so far unobserved S shape is predicted to arise from macroscopic quantum coherent effects including Bloch oscillations.

DOI
10.1103/physrevlett.63.326

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Two-dimensional arrays of very-small-capacitance Josephson junctions have been studied. At low temperatures the arrays show a transition from superconducting to insulating behavior when the ratio of charging energy to Josephson-coupling energy exceeds the value 1. Insulating behavior coincides withthe occurrence of a charging gap inside the BCS gap, with an S-shaped I-V characteristic. This so far unobserved S shape is predicted to arise from macroscopic quantum coherent effects including Bloch oscillations.
We report measurements on two-dimensional arrays of Josephson junctions with junction sizes down to 60 nm by 60nm. Due to their small size, these junctions belong to the class of mesoscopic systems: they show behavior which reveals the underlying quantum mechanical properties. Two energies characterize the junctions, the Josephson energy E (sub j) and the charging energy E (sub c). Arrays in which E (sub j) >> E (sub c) are superconducting around zero bias and at zero temperature, while arrays in which E (sub c) >> E (sub j), called charging arrays, are instead insulating. This is the basis of the superconductor-to-insulator (S-I) transition (Author)
We present observations of charging effects for Cooper pairs in short linear arrays of small-capacitance Josephson junctions. Current-voltage characteristics show a Coulomb gap for Cooper-pair tunneling when the charging energy exceeds the Josephson coupling energy. In a double junction a zero-voltage current is observed that is modulated by a gate voltage applied to the metal island between the junctions. For longer arrays a crossover from Coulomb blockade of Cooper-pair tunneling to a supercurrent is observed when the ratio of Josephson coupling to charging energy is increased.
We have investigated how the transport properties of small-Josephson-junction arrays vary depending on a quantum control parameter (the ratio of the Josephson coupling energy E J to the charging energy E C ), the magnitude of dissipation, and the dimensionality d of the system. We found that the arrays show Coulomb blockade behavior when R S is larger than about d R Q ( R Q ≡ h /4 e 2 =6.45 kΩ) and E J / E C is smaller than a threshold depending on the value of R S and the dimensionality. The result is discussed in terms of quantum phase transition induced by the charging effect and the dissipation.
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.
This thesis describes a number of experiments with superconducting cir- cuits containing small Josephson junctions. The circuits are made out of aluminum islands which are interconnected with a very thin insulating alu- minum oxide layer. The connections form a Josephson junction. The current trough the junction is related to the superconducting phase difference across the junction and described by the well-known Josephson relation. The char- acteristic energy scale for this effect is the Josephson energy, which is a measure for the strength of the coupling of the islands. Due to the parallel plate geometry of the junction a capacitance is formed. This capacitance leads to a charging effect. The characteristic energy scale for this effect is given by the charging energy. With the shadow evaporation technique it is possible to make the Josephson junction area very small and the two characteristic energy scales of the same order of magnitude. Charge and phase are conju- gate variables. Therefore a circuit containing such small Josephson junctions exhibits quantum effects. The microfabrication technique used in this the- sis allows fabrication of solid circuits with controlled quantum mechanical behavior.
For the observation of the charging effect on a Josephson junction, the charging energy (E c) must be much larger than the Josephson coupling energy (E J) and thermal energy (k B T). We investigated the properties of submicron-sized Bi2Sr2CaCu2O8+δ intrinsic Josephson junctions (IJJs) at low temperature. The current–voltage curve of IJJs with a junction area of 0.06 µm2 showed a much higher resistance state near the zero bias voltage regions when the measurement temperature decreased to 72.6 mK. The ratios of E c/E J and E c/k B T were 7.04 and 5.78, respectively, which indicates that the charging effect is dominant. In addition, a characteristic voltage structure due to the charging effect in one-dimensional junction array, which is composed of the offset voltage and the threshold voltage of the junction, was observed.