Full Counting Statistics of Andreev Tunneling

Ville F. Maisi, Dania Kambly, Christian Flindt, and Jukka P. Pekola

Phys. Rev. Lett. 112, 036801 – Published 23 January 2014

Abstract

We employ a single-charge counting technique to measure the full counting statistics of Andreev events in which Cooper pairs are either produced from electrons that are reflected as holes at a superconductor–normal-metal interface or annihilated in the reverse process. The full counting statistics consists of quiet periods with no Andreev processes, interrupted by the tunneling of a single electron that triggers an avalanche of Andreev events giving rise to strongly super-Poissonian distributions.

Received 25 September 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.036801

Authors & Affiliations

Ville F. Maisi^1,2, Dania Kambly³, Christian Flindt³, and Jukka P. Pekola¹

¹Low Temperature Laboratory (OVLL), Aalto University School of Science, P.O. Box 13500, 00076 Aalto, Finland
²Centre for Metrology and Accreditation (MIKES), P.O. Box 9, 02151 Espoo, Finland
³Département de Physique Théorique, Université de Genève, 1211 Genève, Switzerland

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Vol. 112, Iss. 3 — 24 January 2014

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Figure 1
SINIS structure and Andreev processes. (a) A metallic normal-state (N) island (brown) is connected by insulating (I) tunneling barriers to superconducting (S) leads (green). The current $I_{d}$ through a separate single-electron transistor (SET) is sensitive to the charge occupation of the island and is used to read out the number $N$ of excess charges on the island. A copper electrode (yellow) increases the capacitive coupling of the normal-state island to the SET and improves the detector signal-to-noise ratio. (b) An electron above the Fermi level of the normal-state island is reflected as a hole and a Cooper pair is formed in one of the superconductors. Without a voltage across the SINIS, the Fermi energy $E_{F}$ of the normal-state material lies in the middle of the superconducting gap $2 Δ$ .
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Figure 2
FCS of single-electron events. (a) Charging diagram showing Eq. (1) with $N_{g} = 0.5$ . The charge states with $N = 0$ or $N = 1$ excess charges on the island are degenerate. The transitions $0 ⇆ 1$ occur with rate $Γ = 49 Hz$ . Other charge states are energetically unfavorable. (b) Time trace of the current $I_{d}$ in the SET detector, which switches between two levels corresponding to $N = 0$ and $N = 1$ , respectively. (c) Measured FCS of single-electron events for different observation times $t = 10$ , 100, and 1000 ms. Poisson distributions given by Eq. (2) are shown with full lines.
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Figure 3
FCS of Andreev events. (a) Charging diagram showing Eq. (1) with $N_{g} = 0$ . In the ground state, the island is occupied by $N = 0$ excess charges. A single-electron event may bring the island to a state with $N = \pm 1$ excess charges. The excitations $0 \to \pm 1$ occur with the rate $Γ_{u} = 12 Hz$ . Relaxation to the ground state $\pm 1 \to 0$ happens with the rate $Γ_{d} = 252 Hz$ . The transitions $- 1 ⇆ 1$ correspond to Andreev events with the rate $Γ_{A} = 615 Hz$ . (b) Time trace of the SET-detector current $I_{d}$ , which switches between three levels corresponding to $N = - 1$ , $N = 0$ , and $N = 1$ , respectively. (c) Measured FCS of Andreev events for different observation times $t = 10$ , 100, and 1000 ms. Full lines are calculations based on Eqs. (3) and (4). For comparison a Poisson distribution corresponding to 1000 ms is shown with a dashed line.
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Figure 4
Number of Andreev events per avalanche. The full line indicates the theoretical prediction given by Eq. (6) using $Γ_{d} = 252 Hz$ and $Γ_{A} = 615 Hz$ . The inset shows a time trace of the SET-detector current $I_{d}$ during an avalanche with $m = 16$ Andreev events.
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