Three-terminal energy harvester with coupled quantum dots

Journal name:
Nature Nanotechnology
Year published:
Published online

Rectification of thermal fluctuations in mesoscopic conductors is the key idea behind recent attempts to build nanoscale thermoelectric energy harvesters to convert heat into useful electric power1, 2, 3. So far, most concepts have made use of the Seebeck effect in a two-terminal geometry4, 5, 6, 7, 8, where heat and charge are both carried by the same particles. Here, we experimentally demonstrate the working principle of a new kind of energy harvester, proposed recently9, using two capacitively coupled quantum dots. We show that, due to the novel three-terminal design of our device, which spatially separates the heat reservoir from the conductor circuit, the directions of charge and heat flow become decoupled. This enables us to manipulate the direction of the generated charge current by means of external gate voltages while leaving the direction of heat flow unaffected. Our results pave the way for a new generation of multi-terminal nanoscale heat engines.

At a glance


  1. Operating principle of the energy harvester.
    Figure 1: Operating principle of the energy harvester.

    Two quantum dots are capacitively coupled, exchanging energy in packages of U, but not particles. One quantum dot (QDC) is connected to two terminals, L and R. The other (QDG) is coupled to a third terminal, H, which is at a higher temperature. When charge fluctuations occur according to the depicted four-stage sequence, an energy package is extracted from reservoir H and is delivered to the cold subsystem. There, these fluctuations are rectified and converted into a charge current when the product of tunnelling coefficients ΓL0ΓR1 differs from that of the opposite process ΓR0ΓL1 (not shown), that is, when both particle–hole symmetry and left–right symmetry are broken.

  2. Energy harvester device layout and characterization.
    Figure 2: Energy harvester device layout and characterization.

    a, Schematic of the three-terminal device geometry. One electronic reservoir (H, red) is at a high temperature (T + ΔT) and can exchange electrons (green) with quantum dot QDG (yellow disc), as indicated by a red arrow. Two other reservoirs (L and R, blue) at a lower temperature T are tunnel-coupled to another quantum dot (QDC). The quantum dots interact only capacitively (yellow wave) and particle exchange between them is suppressed. b, Schematic of the gate layout (black). Individual gates are denoted by numbers. Gates 1–4 form the heating channel, representing reservoir H, and gates 3–8 form the quantum dot system. Gates PC and PG are used to tune the energies of the dots individually. c, Conductance (G) stability diagram of the quantum dot system for configuration A and TH­ = TL,R = 230 mK. Borders of the stability regions are denoted by red lines (solid and dashed), and regions of stable charge configuration are labelled (NC, NG). d, Cartoon sketches of QDC for two configurations (A and B) of tunnel barrier settings, each corresponding to different products of tunnelling coefficients, ΓL0ΓR1 and ΓL1ΓR0, which leads to different signs for Λ.

  3. 2f current in reservoir R (IR) for configuration A in the vicinity of a TP pair.
    Figure 3: 2f current in reservoir R (IR) for configuration A in the vicinity of a TP pair.

    Black lines denote the stability region borders as obtained from the conductance data. a, Experimental data for 0 < ΔμLR < 10 μV. The signal around the TP pair is a result of thermal gating (regions I–IV). b, The signal becomes reversed if ΔμLR is inverted (−10 μV < ΔμLR < 0). The signal between the TPs is due to the proposed mechanism of energy harvesting. It stays negative, irrespective of the sign of the voltage bias ΔμLR. c, IR as a function of squared heating current between two TPs for slightly different Λ. d, Model calculation for energy-dependent tunnelling barriers of QDC, symmetric with respect to L and R. The signal between the TPs is zero, and only the effect of thermal gating is present. e, Calculation using asymmetric and energy-dependent tunnel barriers as obtained for configuration A with 0 < ΔμLR < 10 μV. f, Model calculations for −10 μV < ΔμLR < 0.

  4. 2f current in reservoir R (IR) for various Λ.
    Figure 4: 2f current in reservoir R (IR) for various Λ.

    a, Measured IR for configuration B. b, Model calculation for configuration B. c, IR for tunnel barriers tuned to symmetric tunnelling coefficients at the Fermi level of the reservoirs. A finite IR is still visible at the centre due to a difference in energy dependence of the confining potential barriers. d, Corresponding model calculations. e, Increasing the gate voltage applied to gate 6 changes the energy dependence of the tunnel barrier connecting QDC to reservoir R. This also inverts the tunnelling asymmetry factor Λ, and the generated charge current therefore changes sign. f, Model calculation for changed energy dependence of tunnelling coefficients.


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Author information

  1. Present address: Kavli Institute of Nanoscience, Faculty of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands

    • Holger Thierschmann


  1. Physikalisches Institut (EP3), Universität Würzburg, Am Hubland, Würzburg D-97074, Germany

    • Holger Thierschmann,
    • Fabian Arnold,
    • Hartmut Buhmann &
    • Laurens W. Molenkamp
  2. Instituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco, Madrid 28049, Spain

    • Rafael Sánchez
  3. Département de Physique Théorique, Université de Genève, Genève 4 CH-1211, Switzerland

    • Björn Sothmann
  4. Institute of Applied Physics, University of Hamburg, Jungiusstrasse 11, Hamburg D-20355, Germany

    • Christian Heyn &
    • Wolfgang Hansen


H.T., H.B. and L.W.M. designed the experiment. C.H. and W.H. provided the wafer material. F.A. fabricated the sample. H.T. and F.A. conducted the measurements. R.S. and B.S. performed the model calculations. All authors discussed the results. H.T., B.S., R.S., H.B. and L.W.M. wrote the manuscript.

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The authors declare no competing financial interests.

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