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arXiv:2404.05890 · Physics Letters A

Current dependence of the low bias resistance of small capacitance Josephson junctions

Venkat Chandrasekhar

Published Apr 10, 2024• 2 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2024.129493

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Quantum fluctuations of the charge at a current-biased Josephson junction and of the Josephson current couple to the quasiparticle tunneling when the system is at equilibrium in the zero-voltage state. The effect of reducing the capacitance of the junction is studied by means of a model Hamiltonian. When this becomes smaller, charge fluctuations are reduced, but the effective dissipation is also lowered so that the junction displays an underdamped behavior. The Josephson branch is shifted at the voltage e/2C because of charging due to the quasiparticles. A path-integral formulation of the model leads to a high dynamical subgap resistance at I\ensuremath{\rightarrow}0, as recently found experimentally.

Physical review. B, Condensed matter•Dec 1, 1989•5 citations
We have measured the current-voltage $(I\ensuremath{-}V)$ characteristics of small-capacitance single Josephson junctions at low temperatures (T=0.02−−0.6K),(T=0.02--0.6\mathrm{K}),(T=0.02−−0.6K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc superconducting quantum interence devices (SQUIDs). The single-junction $I\ensuremath{-}V$ curve is sensitive to the impedance of the environment, which can be tuned in situ. We have observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, where the zero-bias resistance ${R}_{0}^{\ensuremath{'}}$ of the SQUID arrays is much higher than the quantum resistance ${R}_{K}\ensuremath{\equiv}{h/e}^{2}\ensuremath{\approx}26\mathrm{k}\ensuremath{\Omega}.$ The negative differential resistance is evidence of the coherent single-Cooper-pair tunneling within the theory of current-biased single Josephson junctions. Based on this theory, we have calculated the $I\ensuremath{-}V$ curves numerically in order to compare then with the experimental ones at ${R}_{0}^{\ensuremath{'}}\ensuremath{\gg}{R}_{K}.$ The numerical calculation agrees with the experiments qualitatively. We also discuss the ${R}_{0}^{\ensuremath{'}}$ dependence of the single-Josephson-junction $I\ensuremath{-}V$ curve in terms of the superconductor-insulator transition driven by changing the coupling to the environment.
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.
Quantum fluctuations of the charge at a current-biased Josephson junction and of the Josephson current couple to the quasiparticle tunneling when the system is at equilibrium in the zero-voltage state. The effect of reducing the capacitance of the junction is studied by means of a model Hamiltonian. When this becomes smaller, charge fluctuations are reduced, but the effective dissipation is also lowered so that the junction displays an underdamped behavior. The Josephson branch is shifted at the voltage e/2C because of charging due to the quasiparticles. A path-integral formulation of the model leads to a high dynamical subgap resistance at I\ensuremath{\rightarrow}0, as recently found experimentally.