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Giant mesoscopic fluctuations of the elastic cotunneling thermopower of a single-electron transistor

A. S. Vasenko, D. M. Basko, and F. W. J. Hekking
Phys. Rev. B 91, 085310 – Published 27 February 2015
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  • INTRODUCTION
  • QUALITATIVE DISCUSSION AND SUMMARY OF…
  • THE MODEL
  • CALCULATION
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    We study the thermoelectric transport of a small metallic island weakly coupled to two electrodes by tunnel junctions. In the Coulomb blockade regime, in the case when the ground state of the system corresponds to an even number of electrons on the island, the main mechanism of electron transport at the lowest temperatures is elastic cotunneling. In this regime, the transport coefficients strongly depend on the realization of the random impurity potential or the shape of the island. Using random-matrix theory, we calculate the thermopower and the thermoelectric kinetic coefficient and study the statistics of their mesoscopic fluctuations in the elastic cotunneling regime. The fluctuations of the thermopower turn out to be much larger than the average value.

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    • Received 16 December 2014
    • Revised 11 February 2015

    DOI:https://doi.org/10.1103/PhysRevB.91.085310

    ©2015 American Physical Society

    Authors & Affiliations

    A. S. Vasenko1, D. M. Basko1, and F. W. J. Hekking1,2

    • 1University Grenoble Alpes, CNRS, LPMMC, F-38000 Grenoble, France
    • 2Institut Universitaire de France, 103, bd Saint-Michel 75005 Paris, France

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    Issue

    Vol. 91, Iss. 8 — 15 February 2015

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    • Figure 1
      Figure 1

      A sketch of a single-electron transistor. The central island is connected to the source and drain electrodes by tunnel junctions and capacitively coupled to the gate electrode via the gate capacitance Cg. The total capacitance C of the island is given by the sum of the capacitances between the island and each electrode.

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    • Figure 2
      Figure 2

      Schematic view of the dependence of the SET's conductance (a) and thermopower (b) on the dimensionless gate voltage CgVg/e. The three curves in panel (b) correspond to different temperatures, the black solid line corresponding to the highest temperature, the blue dash-dotted line to the lowest.

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    • Figure 3
      Figure 3

      A sketch of possible behavior of the function τ(E) (upper panel) and the corresponding τ2(E) (lower panel), entering Eq. (2a). The scale of the horizontal axis is ∼EC, that of the vertical axis is ∼1.

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    • Figure 4
      Figure 4

      The distribution function P(gT) for x=0 (black solid line) and x=0.3 (red dash-dotted line).

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    • Figure 5
      Figure 5

      The averaged total thermopower with (black solid line) and without (red dashed line) taking into account the elastic cotunneling contiributions. The difference of two curves is most visible in the interval −0.2<x<0.2. See the text for details.

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    • Figure 6
      Figure 6

      An example of pairing 2p+q F's (shown by empty circles) and q F̃'s (filled circles).

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