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Effect of Photon-Assisted Andreev Reflection in the Accuracy of a SINIS Turnstile

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 Added by Angelo Di Marco
 Publication date 2015
  fields Physics
and research's language is English




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We consider a hybrid single-electron transistor (SET) constituted by a gate-controlled normal-metal island (N) connected to two voltage-biased superconducting leads (S) by means of two tunnel junctions (S-I-N-I-S), operated as a turnstile. We show that the exchange of photons between this system and the high-temperature electromagnetic environment where it is embedded enhances Andreev reflection, thereby limiting the single-electron tunneling accuracy.



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We perform a theoretical study of non-equilibrium 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 non-monotonic function of the relaxation rate $Gamma_{mathcal{F}}$ of the distribution function $mathcal{F}(epsilon)$ on the island due to tunneling, as compared to the drive frequency $f$, electron-electron $1/tau_{ee}$ and electron-phonon $1/tau_{eph}$ relaxation rates. Surprisingly, in the strongly non-equilibrium regime, $fgg Gamma_{mathcal{F}}ggtau_{ee}^{-1},tau_{eph}^{-1}$, the turnstile current plateau is recovered, similarly to the ideal equilibrium regime, $tau_{eph}^{-1}gg Gamma_{mathcal{F}}$. The plateau is destroyed in the quasiequilibrium regime when the electron-electron relaxation is faster than tunneling.
One of the typical features of Majorana zero mode (MZM) at the end of topological superconductor is a zero-bias peak in the tunneling spectroscopy of the normal lead-superconductor junction. In this paper we study on a model with one phonon mode coupling to the superconductor lead of the normal lead-superconductor junction, which can be viewed as an electron-lead/phonon-coupled-MZM/hole-lead structure. The phonon-coupled MZM acts as a series of channels in which electron can turn into hole by absorbing and emitting phonons. These channels present in the local density of states (LDOS) as a series of stripes, generating the corresponding peaks in the tunneling spectroscopy. In LDOS, the electron-phonon interaction narrows and redistributes the weight among stripes. In the tunneling spectroscopy, the heights of peaks present a feature of the multi-phonon process. With these investigations, our work illuminates the mechanism of phonon-assisted Andreev reflection at a Majorana zero mode.
We study Andreev reflection in graphene nanoribbon/superconductor hybrid junctions. By using a tight-binding approach and the scattering formalism we show that finite-size effects lead to notable differences with respect to the bulk graphene case. At subgap voltages, conservation of pseudoparity, a quantum number characterizing the ribbon states, yields either a suppression of Andreev reflection when the ribbon has an even number of sites in the transverse direction or perfect Andreev reflection when the ribbon has an odd number of sites. In the former case the suppression of Andreev reflection induces an insulating behavior even when the junction is biased; electron conduction can however be restored by applying a gate voltage.
Coherent charge transport along ballistic paths can be introduced into graphene by Andreev reflection, for which an electron reflects from a superconducting contact as a hole, while a Cooper pair is transmitted. We use a liquid-helium cooled scanning gate microscope (SGM) to image Andreev reflection in graphene in the magnetic focusing regime, where carriers move along cyclotron orbits between contacts. Images of flow are obtained by deflecting carrier paths and displaying the resulting change in conductance. When electrons enter the the superconductor, Andreev-reflected holes leave for the collecting contact. To test the results, we destroy Andreev reflection with a large current and by heating above the critical temperature. In both cases, the reflected carriers change from holes to electrons.
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