The article by Warren Pickett and Mikhail Eremets on room-temperature superconductivity in hydrides had me thinking about the role of specific heat in superconductivity research.

Heike Kamerlingh Onnes and Gilles Holst reported in 1914 that “with respect to the specific heat, nothing peculiar happens” at mercury’s superconducting transition,1 which Kamerlingh Onnes had discovered three years earlier. Twenty years later, after technical advances in cryogenics and thermometry, Kamerlingh Onnes’s former student, Willem Keesom, and J. A. Kok discovered a specific heat jump at the critical temperature Tc, without latent heat.1 It was misinterpreted as a sudden drop in Debye temperature, which assumes phonons are the predominant contributor to specific heat, even though the free electronic model for electronic specific heat (Ce = γT) had been proposed before then. It took almost another 20 years for the superconducting-state electronic specific heat (Ces) to be identified, but still erroneously concluded as having a T3 dependence. Eventually, experimental data covering a wider (Tc/T) range confirmed the exponential-temperature dependence of its electronic origin.2 

In their 1957 article, John Bardeen, Leon Cooper, and J. Robert Schrieffer opened with the statement, “The main facts which a theory of superconductivity must explain are (1) a second-order phase transition at the critical temperature, Tc, (2) an electronic specific heat varying as exp(–T0/T) near T = 0 K and other evidence for an energy gap.”3 The rest is now history.

In my opinion, superconducting hydrides may provide opportunities for studying Ces in detail over an exceptionally broad (Tc/T) range. Intuitively, the near-room-temperature transition would make it impossible to delineate the electronic and the lattice contributions from total specific heat (C = Ce + C) being obtained calorimetrically. That appears to be a valid concern for cuprate superconductors with Tc near or above 90 K. In contrast, for metallic hydrogen with an exceedingly high Debye temperature4 of approximately 3500 K, the lattice specific heat C at 280 K can be estimated to be approximately 1 J/mol K. The same amount of normal-state Ce = γT would also prevail at 280 K if the coefficient γ = 3.6 mJ/mol K2, which is comparable to that of many conventional superconductors.

The difficulty rests with the high-pressure aspect in calorimetric measurements. A standard pressure-cell approach was successfully employed on superconducting uranium some 50 years ago,5 but only at 10 kbar. Researchers are designing and developing diamond anvil cells, but they face challenges regarding pressure limits and heat leak. However, as we look back, after 1911 it took more than 40 years of improving cryogenics and low-temperature calorimetry to finally reveal exponential-temperature dependence of Ces, which was important to the Bardeen-Cooper-Schrieffer theory. We now need to overcome another technical hurdle—in pressure instead of temperature.

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H.
Kamerlingh Onnes
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Commun. Phys. Lab. Univ. Leiden
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L. N.
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N. W.
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W.
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