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STM as a Thermometer

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Theory of Thermodynamic Measurements of Quantum Systems Far from Equilibrium

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Abstract

In Chap. 2 we showed that a measurement of temperature has to be accompanied with a measurement of voltage as well. We discuss here the experimental consequences of the results of Chap. 2. The best spatial resolution so far achieved in thermal imaging of nanoscale conductors is a few nanometers, which is much coarser than routinely achieved for other physical properties. In this chapter, we propose the scanning tunneling thermometer which is capable of mapping sub-angstrom temperature variations in nanoscale conductors. The proposed measurement scheme involves two scanning probe operations to measure the conductance and thermopower, respectively. These two measurements are shown to determine the local temperature with high accuracy in nanoscale conductors where the Wiedemann-Franz law holds quite generally. Our method, if implemented experimentally, would constitute a dramatic improvement of the spatial resolution of scanning thermometry by some two orders of magnitude.

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Notes

  1. 1.

    In a previous version of this dissertation, we used the electron particle current instead of the electrical current. These are equivalent conditions but result in an additional factor of e in defining the linear response coefficient \(\mathcal {L}^{(0)}_{p\alpha }\) in Eq. (4.2).

  2. 2.

    \(\mathcal {L}^{(\nu )}_{p\alpha }\) do not coincide with definitions used in Refs. [31, 32, 34] and Chap. 2: e.g., \(\mathcal {L}^{(0)}_{p\alpha }\) used here has an additional factor of e 2. One factor of e appears since we use electrical current instead of the particle current (see footnote 1). An additional factor of e appears since we write the currents in terms of the bias voltage instead of the bias chemical potential in Eq. (4.2).

  3. 3.

    The Wiedemann–Franz law can be derived explicitly for elastic transport as shown in Appendix C. The first two terms in the Sommerfeld series are shown explicitly.

  4. 4.

    This would be an equivalent realization of our experiment since current conservation would imply that the transmission functions satisfy \(\mathcal {T}_{p\alpha }=\mathcal {T}_{\alpha p}\). In principle, the experiment can be carried out even in the presence of a magnetic flux Φ but, since \(\mathcal {T}_{p\alpha }(\Phi )=\mathcal {T}_{\alpha p}(-\Phi )\), we would have to invert the magnetic field to infer the \(\mathcal {L}^{(\nu )}_{p\alpha }\) coefficients [40].

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Authors and Affiliations

  1. Department of Chemistry, University of Toronto, Toronto, ON, Canada

    Abhay Shastry

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  1. Abhay Shastry
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Shastry, A. (2019). STM as a Thermometer. In: Theory of Thermodynamic Measurements of Quantum Systems Far from Equilibrium. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-33574-8_4

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