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Europhysics Letters (EPL)

Quantum Tunnelling in Small-Capacitance Josephson Junctions in a General Electromagnetic Environment

G. Falci, Vladimir Bubanja, Gerd Schön

Published Sep 1, 1991• 42 citations
Publisher

Abstract

The tunnelling of single electrons in small-capacitance normal tunnel junctions has been shown to be influenced by the fluctuations of the electrodynamic environment. We study the effect of an external circuit with arbitrary impedance on the tunnelling of quasi-particles in voltage-driven Josephson junctions and find even more dramatic effects than in normal junctions. We also discuss the influence of the environment on the tunnelling of Cooper pairs at finite temperatures.

DOI
10.1209/0295-5075/16/1/019

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We have measured the current-voltage $(I\ensuremath{-}V)$ characteristics of small-capacitance single Josephson junctions at low temperatures $(T=0.02--0.6\mathrm{K}),$ 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.

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道生 渡部, David B. Haviland

We have measured the current-voltage characteristics of small-capacitance single Josephson junctions at low temperatures ( T< or =0.04 K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc SQUIDs. We have clearly observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, when the zero-bias resistance of the SQUID arrays is much higher than the quantum resistance h/e(2) approximately 26 kOmega. The negative differential resistance is evidence of coherent single-Cooper-pair tunneling in the single Josephson junction.

arXiv:cond-mat/0103502•Physical Review Letters•May 28, 2001•60 citations
The tunnelling of single electrons in small-capacitance normal tunnel junctions has been shown to be influenced by the fluctuations of the electrodynamic environment. We study the effect of an external circuit with arbitrary impedance on the tunnelling of quasi-particles in voltage-driven Josephson junctions and find even more dramatic effects than in normal junctions. We also discuss the influence of the environment on the tunnelling of Cooper pairs at finite temperatures.
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.
This thesis presents the results of an experimental study onsmall-capacitance Josephson junctions in a high impedanceenvironment. In small-capacitance Josephson junctions the charging energyEC=e2/2C becomes relevant at low temperature and thecharging effects influence the transport properties. In theobservation of single-charge effects, a fundamental role isplayed by the impedance Z(ω) of the electromagneticenvironment surrounding the junction. To detect the tunnelingof single Cooper pairs in one junction, it is essential toembed the junction in a high impedance environment at all thefrequencies, such that Z(ω)>>RQ, where RQ=h/(2e)2= 6.45 kΩ is the quantum resistance forCooper pairs. This requirement is necessary in order to avoidthe fast discharge of the junction capacitance through theexternal circuit. In this work the effect of the high impedance environment isstudied on Cooper pair transistors (CPT) and single junctionswith tunable coupling (SQUID). The high impedance environmentis obtained by biasing the sample under test with four SQUIDarrays. The SQUID geometry, besides the modulation of thejunctions Josephson energy (EJ), allows the tuning in situ of the effective impedanceof the environment. By applying a magnetic field perpendicularto the SQUIDs loop, the zero bias resistance of the leads (R0) can be varied over several orders of magnitude(104<R0 (Ω)<108), providing the possibility to study the samesample in different electromagnetic environments. Measurements of the current-voltage (I-V) characteristic ofa single junction with SQUID geometry allow the investigationof the influence of both the electrodynamic environment and theEJ/ECratio in the same sample. As the impedance of thebiasing leads is increased (R0>>RQ), the I-V curve of the junction exhibits a welldefined Coulomb blockade feature with a region of negativedifferential resistance, evidence of the coherent tunneling ofsingle Cooper pairs. Measurements on CPT samples also show how the Coulombblockade feature in the I-V curve becomes sharper as theimpedance of the environment is increased. Furthermore theyindicate how the Coulomb blockade threshold voltage is modifiedwith the DC signal applied to the gate. When the SQUID arraysare highly resistive, the gate-induced modulation of the I-Vcurve changes frome-periodic to 2e-periodic, suggesting that high impedance leadseffectively reduce non-equilibrium quasiparticle poisoning.
The current-voltage characteristics of ultrasmall Josephson junctions sensitively depend on the electromagnetic environment of the junction. When the charging energy exceeds the Josephson coupling energy, the usual supercurrent at zero voltage is completely suppressed. However, for typical environmental impedances, which are small compared to the resistance quantum, stochastic Cooper-pair tunneling leads to a supercurrent peak at a small finite voltage which is proportional to the temperature and the low-frequency resistance of the external circuit. An analytic expression for the form of this universal peak, which is independent of the high-frequency behavior of the environment, is given. With increasing Josephson coupling the peak merges into the usual supercurrent of a Josephson junction. At larger voltages the Cooper-pair current depends on details of the environment. Current peaks are shown to result from resonances in the environmental impedance. Specifically, the case of an LC transmission line of finite length is discussed.
The number of Cooper pairs on a small superconducting island coupled to superconducting leads by a Josephson junction fluctuates due to tunneling of Cooper pairs through the junction. On the other hand, the impedance of the circuit surrounding the island tends to suppress these fluctuations and to restore charge quantization. We consider the influence of the electromagnetic environment within a two-state approximation for the charge on the island. The average charge and the slope of the steps of the Coulomb staircase are calculated for a realistic environmental impedance and finite temperatures in the range of current experimental studies. It is shown that even a low-frequency environment may lead to a considerable reduction of charge fluctuations provided the integrated total impedance is large enough.
This thesis presents the results of an experimental study on single-charge effects in nanoscale Josephson junctions and Cooper pair transistors (CPTs). In nanoscale Josephson junctions the charging energy EC becomes significant at sub-Kelvin temperatures and single-charge effects, such as the Coulomb blockade of Cooper pair tunneling, influence the transport properties. In order to observe charging effects in a single Josephson junction, the impedance of the electromagnetic environment surrounding the junction has to be larger than the quantum resistance (RQ=h/4e2≈6.45kΩ). In this work the high impedance environment is obtained by biasing the sample under test (single Josephson junction or CPT) with four one-dimensional Josephson junction arrays having SQUID geometry. The advantage of this configuration is the possibility of tuning in situ the effective impedance of the electromagnetic environment. By applying a magnetic field perpendicular to the SQUID loops, the Josephson energy EJ of the SQUIDs is suppressed, resulting in an increase of the measured zero bias resistance of the arrays of several orders of magnitude (104< R0 (Ω) <109). This bias method enables the measurement of the same sample in environments with different impedance. As the impedance of the environment is increased, the current-voltage characteristics (IVCs) of the single Josephson junction and of the CPT show a well defined Coulomb blockade feature with a region of negative differential resistance, signature of the coherent tunneling of single Cooper pairs. The measured IVCs of a single Josephson junction with SQUID geometry in the high impedance environment show a qualitative agreement with the Bloch band theory as the EJ/EC ratio of the junction is tuned with the magnetic field. We also studied a single nontunable Josephson junction with strong coupling (EJ/EC > 1), where the exact dual of the overdamped Josephson effect is realized, resulting in a dual shape of the IVC, where the roles of current and voltage are exchanged. Here, we make for the first time a detailed quantitative comparison with a theory which includes the effect of fluctuations due to the finite temperature of the environment. The measurements on CPTs in the high impedance environment showed that the Coulomb blockade voltage is modulated periodically by the gate-induced charge. The gate-voltage dependence of the CPT changes from e-periodic to 2e-periodic as the impedance of the environment is increased. The high impedance environment reduces quasiparticle tunneling rates, thereby restoring the even parity of the CPT island. This behavior suggests that high impedance leads can be used to effectively suppress quasiparticle poisoning.
We have measured the current-voltage characteristics of small-capacitance single Josephson junctions at low temperatures ( T< or =0.04 K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc SQUIDs. We have clearly observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, when the zero-bias resistance of the SQUID arrays is much higher than the quantum resistance h/e(2) approximately 26 kOmega. The negative differential resistance is evidence of coherent single-Cooper-pair tunneling in the single Josephson junction.