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Physical Review Applied

Suppression of Back-Tunneling Events in Hybrid Single-Electron Turnstiles by Source-Drain Bias Modulation

Marco Marín‐Suárez, Yu. A. Pashkin, Joonas T. Peltonen, Jukka P Pekola

Published Apr 27, 2023• 0 citations
Publisher

Abstract

The accuracy of single-electron currents produced in hybrid turnstiles at high operation frequencies is, among other errors, limited by electrons tunneling in the wrong direction. Increasing the barrier transparency between the island and the leads, together with the source-drain bias, helps to suppress these events in a larger frequency range, although they lead to some additional errors. We experimentally demonstrate a driving scheme that suppresses tunneling in the wrong direction, thus extending the range of frequencies for generating accurate single-electron currents. The main feature of this approach is an additional ac signal applied to the bias with frequency twice that applied to the gate electrode. This allows additional modulation of the island chemical potential. By using this approach under certain parameters, we improve the single-electron current accuracy by one order of magnitude. Finally, we show through experimentally contrasted calculations that our method can improve accuracy even in devices for which the usual gate driving gives errors of the order of ${10}^{\ensuremath{-}3}$ at high frequencies and can bring them under $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$.

DOI
10.1103/physrevapplied.19.044088

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The accuracy of single-electron currents produced in hybrid turnstiles at high operation frequencies is, among other errors, limited by electrons tunneling in the wrong direction. Increasing the barrier transparency between the island and the leads, together with the source-drain bias, helps to suppress these events in a larger frequency range, although they lead to some additional errors. We experimentally demonstrate a driving scheme that suppresses tunneling in the wrong direction, thus extending the range of frequencies for generating accurate single-electron currents. The main feature of this approach is an additional ac signal applied to the bias with frequency twice that applied to the gate electrode. This allows additional modulation of the island chemical potential. By using this approach under certain parameters, we improve the single-electron current accuracy by one order of magnitude. Finally, we show through experimentally contrasted calculations that our method can improve accuracy even in devices for which the usual gate driving gives errors of the order of 10\ensuremath−3{10}^{\ensuremath{-}3}10\ensuremath−3 at high frequencies and can bring them under 5\ifmmode×\else\texttimes\fi10\ensuremath−45\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}5\ifmmode×\else\texttimes\fi10\ensuremath−4.
Accuracy of single-electron currents produced in hybrid turnstiles at high operation frequencies is, among other errors, limited by electrons tunnelling in the wrong direction. Increasing the barrier transparency between the island and the leads, and the source-drain bias helps to suppress these events in a larger frequency range, although they lead to some additional errors. We experimentally demonstrate a driving scheme that suppresses tunnelling in the wrong direction hence extending the range of frequencies for generating accurate single-electron currents. The main feature of this approach is an additional AC signal applied to the bias with twice the frequency as the one applied to the gate electrode. This allows additional modulation of the island chemical potential. By using the new approach under certain parameters, we improve the single-electron current accuracy by one order of magnitude. Finally, we show through experimentally-contrasted calculations that our method can improve accuracy even in devices for which the usual gate driving gives errors ∼10−3\sim 10^{-3}∼10−3 at high frequencies and can bring them under 5×10−45\times 10^{-4}5×10−4.
First I discuss various candidates of single-electron current pumps for quantum metrology. Then I focus on the hybrid normal-metal-superconductor turnstile in the form of a one-island single-electron transistor with one gate. The device demonstrates robust current plateaus at multiple levels of ef at frequency f. I discuss the various error mechanisms, based on our experiments and theoretical considerations. Ultimately the quantization accuracy is expected to be limited by either two-electron tunneling or by Cooper-pair-electron co-tunneling. We predict that it should be possible to achieve the metrological accuracy of 10-8, while maintaining the quantized current on the level of more than 10 pA, just by one turnstile with realistic parameters using aluminium as a superconductor. Recently we have managed to run ten turnstiles in parallel increasing the current level to above 100 pA. Work on suppressing the harmful sub-gap leakage current is in progress with encouraging experimental results.
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.
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 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.