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Measurements on Two-Dimensional Arrays of Mesoscopic Josephson Junctions

T. S. Tighe

Published Feb 1, 1993• 0 citations
OpenAlex

Abstract

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)

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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 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.
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.
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.
We review experiments on small-capacitance Josephson junctions. When the Josephson junction is fabricated in the configuration of dc superconducting quantum interference device (SQUID), the Josephson coupling can be tuned IN SITU with an external magnetic field. The electrical transport properties of one-dimensional arrays of small-capacitance dc SQUIDs have been investigated in order to study the superconductor-insulator transition. The arrays have also been used to bias a single Josephson junction, and a clear Coulomb blockade of Cooper-pair tunneling has been observed in the single junction.
We study the superconductor-insulator transition of a two-dimensional Bose-Hubbard model, considering as a specific example, an array of Josephson junctions. Within a coarse-graining approach we derive an effective free-energy functional from which we determine the phase diagram. At zero temperature it consists of a superconducting phase and Mott-insulating lobes. The phase boundaries of some of these lobes display reentrant behavior as a function of temperature. Next, we evaluate the electromagnetic-response functions of the system. The real part of the longitudinal conductivity is characterized by an excitation gap, whereas the imaginary part describes a capacitor. In an ideal system, under certain conditions a universal conductance is found at the transition. If we add low-frequency dissipation to the model a different value of the universal conductance is found, but still it is independent of the strength of the dissipation. Qualitatively differing results are obtained for frustrated and unfrustrated systems. We also discuss the Hall conductance of the system.
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.