in turn is also responsible for the validity of the
Wiedemann-Franz law. However, the opposite is
not true: The validity of the Wiedemann-Franz law
is a consequence of the smooth energy dependence
of the electronic transmission (35, 36), but this does
not imply that thermal transport is quantized in all
cases. For example, our simulations of the Pt atomic junctions suggest that although the electrical and
thermal conductance traces show discrete steps
and are in agreement with the Wiedemann-Franz
law (Fig. 4A), one should not expect electrical or
thermal conductance quantization (20). Even a
single-atom contact of Pt sustains multiple conduction channels with intermediate transmissions
between 0 and 1 that contribute to the transport
properties (Fig. 4B), which is at variance with the
Au case. These additional channels originate from
the contribution of d-orbitals in Pt (11). Further,
our simulations show that the electrical and thermal conductance histograms for Pt are relatively
featureless and that there are no strongly preferred
conductance values at room temperature (20).
To unambiguously test these predictions, we
performed measurements with a Pt-coated scann-
ing probe and a Pt substrate, using the same meth-
odology that we used for Au atom junctions. The
measured electrical and thermal conductance traces
(Fig. 4C) show plateaus. A histogram-based analysis
of 100 Pt traces (Fig. 4D) revealed that the Lorenz
ratio is very close to 1 and therefore obeys the
Wiedemann-Franz law. However, histograms of
electrical and thermal conductance traces do not
show conductance quantization (20), in agreement
with our computational predictions. This demon-
strates that thermal conductance quantization is
not a universal feature of all metallic systems at
Our work provides insights into thermal transport in atomic-size Au and Pt contacts and reveals
conductance quantization at room temperature in
Au atom junctions. We have also established the applicability of the Wiedemann-Franz law for analyzing thermal transport in metallic atomic-size contacts.
The scanning calorimetric probes described here
will enable thermal transport studies in molecular
junctions, 1D chains of atoms, and individual polymer chains, all of which have been studied theoretically and computationally for more than half a
century (13, 37) but have not been probed experimentally because of the lack of experimental tools.
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P.R. acknowledges support from the U.S. Department of Energy
Basic Energy Sciences program (award no. DE-SC0004871). P.R.
and E.M. acknowledge support from the U.S. Office of Naval
Research (N00014-16-1-2672) and the U.S. National Science
Foundation (CBET 1235691). J.C.C. acknowledges funding from
the Spanish Ministry of Economy, Industry and Competitiveness
(contract no. FIS2014-53488-P) and thanks the German Research
Foundation (DFG) and Collaborative Research Center (SFB) 767
for sponsoring his stay at the University of Konstanz as a Mercator
Fellow. M.M. and P.N. acknowledge funding from the SFB 767 and
computer time granted by the John von Neumann Institute for
Computing and the bwHPC framework program of the State of
Baden-Württemberg, Germany. J.C.K. and F.P. were financially
supported by the Carl Zeiss Foundation, the SFB 767 of the DFG,
and the Junior Professorship Program of the Baden-Württemberg
Ministry of Science, Research, and the Arts. We acknowledge the
Lurie Nanofabrication Facility for facilitating the fabrication of
devices. All of the data are available in the main paper and the
Materials and Methods
Figs. S1 to S10
Movies S1 to S6
27 December 2016; accepted 6 February 2017
Published online 16 February 2017
Fig. 4. Calculated and measured transport properties of Pt atomic junctions. (A) Representative
traces of the electrical conductance (blue) and the electronic thermal conductance (red) for Pt junctions,
calculated by combined MD and transport simulations. (B) The total electronic transmission and the
individual electronic transmission coefficients as a function of the energy (measured with respect to the
Fermi energy EF) for the contact geometry shown in the inset. The electronic transmission has
substantive contributions from three channels at the Fermi level. In addition, the transmission varies
more rapidly with energy than for Au atomic junctions. (C) Representative measured traces of electrical
(blue) and thermal (red) conductances for Pt atomic junctions show discrete steps (conductance
histograms do not display electrical or thermal conductance quantization) (20). (D) Histogram similar to
that shown in Fig. 2F but for Pt data, showing that the Wiedemann-Franz law is applicable (the peak is at
1.04). The corresponding theoretical results can be seen in fig. S10 (20).