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Physical Review B

Suppression of Cooper-pair tunneling in superconducting charge boxes in tunable electromagnetic environments

Watson Kuo, Cen-Shawn Wu, Jia-Hong Shyu, C. D. Chen

Published Jan 11, 2007• 2 citations
Publisher

Abstract

The Cooper-pair tunneling in superconducting charge boxes in tunable electromagnetic environments is experimentally studied using a single-electron-transistor electrometer and via current-voltage characteristics measurement with small excitations. In the low-impedance regime, the environmental effect is quantified with an effective Josephson coupling energy, which is found to decrease as the environment impedance increases. In the high-impedance regime, the Cooper-pair tunneling is blockaded. For impedance above $250\phantom{\rule{0.3em}{0ex}}\mathrm{M}\ensuremath{\Omega}$, Coulomb oscillation of the zero-bias conductance suggests that Cooper-pair tunneling is completely suppressed and subgap quasiparticle tunneling becomes dominant.

DOI
10.1103/physrevb.75.014517

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The Cooper-pair tunneling in superconducting charge boxes in tunable electromagnetic environments is experimentally studied using a single-electron-transistor electrometer and via current-voltage characteristics measurement with small excitations. In the low-impedance regime, the environmental effect is quantified with an effective Josephson coupling energy, which is found to decrease as the environment impedance increases. In the high-impedance regime, the Cooper-pair tunneling is blockaded. For impedance above 250M\ensuremathΩ250\phantom{\rule{0.3em}{0ex}}\mathrm{M}\ensuremath{\Omega}250M\ensuremathΩ, Coulomb oscillation of the zero-bias conductance suggests that Cooper-pair tunneling is completely suppressed and subgap quasiparticle tunneling becomes dominant.
We have measured the Cooper pair transistor (CPT) in a tunable electromagnetic environment consisting of four one-dimensional superconducting quantum interference device arrays. The transport properties of the CPT in the high impedance limit, ${Z}_{\mathrm{env}}⪢{R}_{Q}\ensuremath{\simeq}6.45\phantom{\rule{0.3em}{0ex}}\mathrm{k}\ensuremath{\Omega}$, are studied for different ratios of the Josephson coupling energy to the charging energy. As the impedance of the environment is increased, the current-voltage characteristic (IVC) of the CPT develops a Coulomb blockade of Cooper pair tunneling and the measured IVCs agree qualitatively with a theory based on quasicharge dynamics for a CPT. Increasing the impedance of the environment induces a transition in the modulation of the IVC with the gate charge from eee-periodic to 2e2e2e-periodic.
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.
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.
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.
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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−−0.6K),(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.