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arXiv:1106.3918 · Europhysics Letters (EPL)

Andreev tunneling in charge pumping with SINIS turnstiles

Thomas Aref, V. F. Maisi, M. Gustafsson, Per Delsing, Jukka P Pekola

Published Oct 13, 2011• 22 citations
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Abstract

We present measurements on hybrid single-electron turnstiles with superconducting leads contacting a normal island (SINIS). We observe Andreev tunneling of electrons influencing the current plateau characteristics of the turnstiles under radio-frequency pumping. The data is well accounted for by numerical simulations. We verify the dependence of the Andreev tunneling rate on the turnstile's charging energy. Increasing the charging energy effectively suppresses the Andreev current.

DOI
10.1209/0295-5075/96/37008

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We present measurements on hybrid single-electron turnstiles with superconducting leads contacting a normal island (SINIS). We observe Andreev tunneling of electrons influencing the current plateau characteristics of the turnstiles under radio-frequency pumping. The data is well accounted for by numerical simulations. We verify the dependence of the Andreev tunneling rate on the turnstile's charging energy. Increasing the charging energy effectively suppresses the Andreev current.
We consider the influence of the electromagnetic fluctuations on the transport properties of a hybrid single electron transistor, consisting of superconducting electrodes and a normal-metal island, when operated as a turnstile. We derive the analytic expressions for the rates near the thresholds of single electron tunneling, Andreev reflection, and Cooper-pair–electron cotunneling processes. These results show that the dissipative on-chip impedance suppresses the rates of the undesirable higher-order tunneling processes much stronger than the single electron tunneling which can therefore be utilized to increase the accuracy of such a device in quantum metrological applications.
We present an experimental study of hybrid turnstiles with high charging energies in comparison to the superconducting gap. The device is modeled with the sequential tunneling approximation. The backtunneling effect is shown to limit the amplitude of the gate drive and thereby the maximum pumped current of the turnstile. We compare results obtained with sine and square wave drive and show how a fast rise time can suppress errors due to leakage current. Quantized current plateaus up to 160 pA are demonstrated.
We perform a theoretical study of nonequilibrium effects in charge transport through a hybrid single-electron transistor based on a small normal metal (N) island with the gate-controlled number of electrons, tunnel-coupled to voltage-biased superconducting (S) electrodes (SINIS). Focusing on the turnstile mode of the transistor operation with the gate voltage driven periodically, and electrons on the island being out of equilibrium, we find that the current quantization accuracy is a nonmonotonic function of the relaxation rate ${\mathrm{\ensuremath{\Gamma}}}_{\mathcal{F}}$ of the distribution function $\mathcal{F}(\ensuremath{\epsilon})$ on the island due to tunneling, as compared to the drive frequency fff, electron-electron $1/{\ensuremath{\tau}}_{ee}$, and electron-phonon $1/{\ensuremath{\tau}}_{eph}$ relaxation rates. Surprisingly, in the strongly nonequilibrium regime, $f\ensuremath{\gg}{\mathrm{\ensuremath{\Gamma}}}_{\mathcal{F}}\ensuremath{\gg}{\ensuremath{\tau}}_{ee}^{\ensuremath{-}1},{\ensuremath{\tau}}_{eph}^{\ensuremath{-}1}$, the turnstile current plateau is recovered, similarly to the ideal equilibrium regime, ${\ensuremath{\tau}}_{eph}^{\ensuremath{-}1}\ensuremath{\gg}{\mathrm{\ensuremath{\Gamma}}}_{\mathcal{F}}$. The plateau is destroyed in the quasiequilibrium regime when the electron-electron relaxation is faster than tunneling.
We present an experimental study of hybrid turnstiles with high charging energies in comparison to the superconducting gap. The device is modeled with the sequential tunneling approximation. The backtunneling effect is shown to limit the amplitude of the gate drive and thereby the maximum pumped current of the turnstile. We compare results obtained with sine and square wave drive and show how a fast rise time can suppress errors due to leakage current. Quantized current plateaus up to 160 pA are demonstrated.
Single electron pumping by a SINIS turnstile is investigated up to 1 GHz in various conditions to realize a quantum current standard. A standard deviation of the pumping current at 100 MHz is about 10-4at base temperature of a dilution refrigerator. As expected, the plateau of the pumped current degrades as temperature increases because of the thermal smearing of Fermi energy of a normal metal island. On the other hand, an externally applied magnetic fields dramatically suppresses excess current on the single electron pumping plateau. This originates from the quasiparticle relaxation enhancement due to the penetration of the magnetic vortices into the superconducting leads.
We study theoretically current quantization in the charge turnstile based on the superconductor-normal-metal single-electron transistor. The quantization accuracy is limited by either Andreev reflection or by Cooper-pair-electron cotunneling. The rates of these processes are calculated in the "above-the-threshold" regime when they compete directly with the lowest-order tunneling. By shaping the ac gate voltage drive it should be possible to achieve the metrological accuracy of 10;{-8}, while maintaining the quantized current on the level of 30 pA, just by one turnstile with realistic parameters using aluminum as a superconductor.