Abstract
<title>Abstract</title> <p>Over the course of six decades numerous thermal heat transport measurements across a normal-metal to superconductor interface have shown that attributing this transport exclusively to lattice vibrations (phonons), typically taken proportional to the cube of the temperature (\(\:{T}^{3}\)), is inadequate. These researchers deemed their results inexplicable, but stating that extra heat transport as carried by electrons would be a likely transport mechanism. Examining the historical thermal data taken on eleven different samples is here compared against four sets of theoretical models that could account for the electronic component: (1) Andreev transport, (2) thin oxide tunneling as proposed by Griffin and Maki, (3) tunneling across an insulating layer as expounded by Giaever and Megerle, and (4) electron scattering at interfacial defects or impurities as considered by Bardeen, Rickayzen, and Teword (BRT). In the cases of the Giaever-Megerle and BRT, determination of the interfacial thermal conductances is newly presented here by means of combination with the Wiedemann-Franz (WF) law as applied to interfaces. Thermal transport is analyzed as the sum of the parallel phonon and electron components across the boundary. Below approximately 20% of \(\:{T}_{c}\) interfacial heat transport is dominated by phonons, and it is seen in this work that the contribution due to electrons will often exceed that of the phonon contribution starting at 30% of \(\:{T}_{c}\) and dominates above 50%. For 0.2 < \(\:{T/T}_{c}\)< 0.5 both transport mechanisms must be accounted for to align with experiment. This comparison shows that of the four examined interfacial electronic transport models, that of Griffin and Maki does not align well with experiment, that of Andreev can align only if the contacting normal-metal to superconductor area is reduced to a scale 1% or smaller of the physical area and completely fails near and above \(\:{T}_{c}\). Using the interfacial WF law, both adaptations of Giaever-Megerle and BRT enable calculation of the interfacial thermal conductance continuously above and below \(\:{T}_{c}\). Fitting these theoretical models to the experimental thermal data indicates that it is possible that more than one electronic heat transport mechanism may be present simultaneously in some combination. When selecting only one electronic transfer model to combine with the phonon transport, the BRT as adapted using the interfacial WF law requires only a single input, described here as an electrical contact resistance, to adequately cover the full range of temperatures from above \(\:{T}_{c}\) in the fully normal state down through \(\:{T}_{c}\) and below.</p>