Phase sensitive electron-phonon coupling in a superconducting proximity structure

T. T. Heikkilä and Francesco Giazotto

Phys. Rev. B 79, 094514 – Published 11 March 2009

Abstract

We study the role of the superconducting proximity effect on the electron-phonon energy exchange in diffusive normal metals (N) attached to superconductors (S). The proximity effect modifies the spectral response of the normal metal, in particular the local density of states. This leads to a weakening of the electron-phonon energy relaxation. We show that the effect is easily observable with modern thermometry methods and predict that it can be tuned in structures connected to multiple superconductors by adjusting the phase difference between superconducting order parameters at the two NS interfaces.

Received 27 October 2008

DOI:https://doi.org/10.1103/PhysRevB.79.094514

Authors & Affiliations

T. T. Heikkilä^*

Low Temperature Laboratory, Helsinki University of Technology, P.O. Box 5100, FIN-02015 TKK, Espoo, Finland

Francesco Giazotto

NEST CNR-INFM and Scuola Normale Superiore, I-56126 Pisa, Italy

^*tero.heikkila@tkk.fi

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Vol. 79, Iss. 9 — 1 March 2009

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Images

Figure 1
Schematic structure considered in this paper: the superconducting electrodes (assumed to be large and residing at the phonon temperature $T_{p}$ ) induce a proximity effect into the normal metal. This proximity effect changes the spectrum of the electronic excitations and thereby also the electron-phonon energy exchange ${\dot{Q}}_{e-p}$ . The spectrum can be controlled via the phase difference $ϕ$ of the superconducting order parameter. This allows one to explore the effect as shown below in Fig. 6.Reuse & Permissions
Figure 2
(Color online) Phase and energy dependences of the electron-phonon scattering rate $Γ_{e-p}$ normalized to the normal-state zero-energy result $Γ_{e-p}^{N} = 7 λ ζ (3) {(k_{B} T)}^{3}$ at two different temperatures (top: $k_{B} T = E_{Th} / 2$ ; bottom: $k_{B} T = 5 E_{Th}$ ). We have assumed $Δ_{0} = 20 E_{Th}$ and averaged the rates across the normal-metal piece. The solid line shows the energy dependence obtained in the normal case for which $K (ϵ, ω) = 1$ . Note the logarithmic scale of the figure. The exact low-energy values in the presence of the proximity effect depend on the magnitude of the inelastic-scattering parameter $γ$ in Eq. (2). Here and throughout we have chosen $γ = 10^{- 5} E_{Th}$ .Reuse & Permissions
Figure 3
(Color online) Position- and temperature-dependent heat current density $P_{e-p}$ between the electron and phonon systems inside the normal part of the SNS system of length $L$ . Here $ϕ = 0$ , $Δ = 20 E_{Th}$ , $T_{p} = 0$ , and the heat current density has been normalized to the normal-state value $P_{e-p}^{N} = Σ T_{e}^{5}$ .Reuse & Permissions
Figure 4
(Color online) Dependence of the heat current on electron temperature and the length $L$ of the junction compared to the zero-temperature coherence length $ξ_{0} = \sqrt{ℏ D / Δ}$ . Here $ϕ = 0$ and $T_{p} = 0$ .Reuse & Permissions
Figure 5
(Color online) Phase-dependent electron-phonon heat current at a few different temperatures with $T_{p} = 0$ and $Δ = 20 E_{Th}$ . The closing minigap for $ϕ \to π$ shows up as a rapid increase in ${\dot{Q}}_{e-p}$ at low temperatures. For $k_{B} T_{e}$ somewhat larger than the minigap, the phase dependence becomes much weaker although the overall heat current is still smaller than in the normal state.Reuse & Permissions
Figure 6
(Color online) (a) Scheme of a possible experimental setup. A radio-frequency (rf) SQUID containing a SNS junction is threaded by a magnetic flux $Φ$ which allows one to tune the electron-phonon interaction in the N region. Additional superconducting electrodes tunnel coupled to the N wire allow one to probe the averaged phase-dependent ${\dot{Q}}_{e-p} (T_{e}, T_{p}, ϕ)$ . These serve both as heaters (h) and thermometers (th). (b) Sketch of the thermal model of the N wire (see text). (c) Steady-state electron temperature inside the SNS junction as a function of the phase for a few driving powers at a phonon temperature $T_{p} = E_{Th} / (2 k_{B})$ . For this curve, we chose $E_{Th} / k_{B} = 100 mK$ (see text).Reuse & Permissions

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