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Thermal Conductance of a Single-Electron Transistor

B. Dutta, J. T. Peltonen, D. S. Antonenko, M. Meschke, M. A. Skvortsov, B. Kubala, J. König, C. B. Winkelmann, H. Courtois, and J. P. Pekola
Phys. Rev. Lett. 119, 077701 – Published 15 August 2017
Physics logo See Synopsis: Transistor Breaks Law of Thermal Conductivity
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    Abstract

    We report on combined measurements of heat and charge transport through a single-electron transistor. The device acts as a heat switch actuated by the voltage applied on the gate. The Wiedemann-Franz law for the ratio of heat and charge conductances is found to be systematically violated away from the charge degeneracy points. The observed deviation agrees well with the theoretical expectation. With a large temperature drop between the source and drain, the heat current away from degeneracy deviates from the standard quadratic dependence in the two temperatures.

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    • Received 11 April 2017

    DOI:https://doi.org/10.1103/PhysRevLett.119.077701

    © 2017 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Coulomb blockadeThermal conductivity
    Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

    Synopsis

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    Transistor Breaks Law of Thermal Conductivity

    Published 15 August 2017

    A single-electron transistor carries more heat than that predicted by the Wiedemann-Franz law linking thermal and electrical conductivities.

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    Authors & Affiliations

    B. Dutta1, J. T. Peltonen2, D. S. Antonenko3,4,5, M. Meschke2, M. A. Skvortsov3,4,5, B. Kubala6, J. König7, C. B. Winkelmann1, H. Courtois1, and J. P. Pekola2

    • 1Université Grenoble Alpes, CNRS, Institut Néel, 25 Avenue des Martyrs, 38042 Grenoble, France
    • 2Low Temperature Laboratory, Department of Applied Physics, Aalto University School of Science, P.O. Box 13500, 00076 Aalto, Finland
    • 3Skolkovo Institute of Science and Technology, Skolkovo, 143026 Moscow, Russia
    • 4L. D. Landau Institute for Theoretical Physics, 142432 Chernogolovka, Russia
    • 5Moscow Institute of Physics and Technology, Moscow, 141700, Russia
    • 6Institute for Complex Quantum Systems and IQST, University of Ulm, 89069 Ulm, Germany
    • 7Theoretische Physik and CENIDE, Universität Duisburg-Essen, 47048 Duisburg, Germany

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    Issue

    Vol. 119, Iss. 7 — 18 August 2017

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    Images

    • Figure 1
      Figure 1

      A single-electron transistor and the setup for the heat transport measurement. (a) False-colored SEM image of the full device. The circuit in red indicates the charge transport setup, while the black one stands for the heat transport setup. (b) Schematic of the device, with the different elements shown in colors. (c) Enlarged view of the central part of the SET. (d) Differential conductance map of the sample A SET at 50 mK against drain-source voltage VSET and induced charge ng.

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    • Figure 2
      Figure 2

      Left: Variation of electronic temperature Te of the sample B source with cooler bias voltage, at gate open (ng=0.5) and gate closed (ng=0) states, at a bath temperature Tb of 152 mK. The full line is a fit of the gate-open state data; see the text. Right: Temperature modulation by the gate voltage expressed in terms of induced charge ng in the heating regime (top) and in the cooling regime (bottom) at cooler bias points indicated by the blue and red arrows in the left plot.

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    • Figure 3
      Figure 3

      Top: Thermal (blue dots) and charge (green dots) conductances of the SET at a bath temperature of 132 (left, sample A) and 152 mK (right, sample B) in units of the conductances in the gate-open state κ0 and σ0. The thermal flow through the SET was calculated assuming that the Wiedemann-Franz law is fulfilled at the gate-open state. The charge transport was measured at a bias of 22.4 (sample A) and 19.2  μV (sample B). The heat transport data were acquired by cooling the source electronic bath by 30 (sample A) and 22 mK (sample B) below the bath temperature. Bottom: Lorenz ratio (purple dots) defined as L/L0, where L=κ/(σTm) for sample A (left) and sample B (right). The error bars are related to the uncertainty in the temperature measurement. The Wiedemann-Franz law sets L=L0. The red line is the theoretical prediction based on Ref. [19].

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    • Figure 4
      Figure 4

      Nonlinear heat flow through the sample B SET at different gate states as a function of the difference of the squared temperatures between the source and the bath (symbols) together with power-law fits (full lines). The slopes are 1.00, 1.10, and 1.14, respectively, at gate positions ng=0.5, 0.3, and 0. The unit slope expected for the linear regime of heat transport is shown as dotted gray lines.

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