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I am currently studying the Debye model and I've found out that for two-dimensional materials the specific heat in low temperature limit should scale with temperature as ~T$^2$ as opposed to the "usual" ~T$^3$ in case of 3-D solids.

Now I'm wondering how well the 2-D Debye model acutally predicts reality (especially for graphene) but I have a hard time finding experimental data on the topic.

I found a paper from 2012 (Thermal properties of graphene: Fundamentals and applications by E. Pop, V. Varshney and AK. Roy), where the authors explicitly say that the specific heat of graphene has not been measured directly. It's been seven years now since the paper was published, so maybe something has changed? And if it hasn't, why is it so difficult to measure graphene's specific heat?

I've also noticed there is a related question here but all the answers cite papers about thermal diffusivity. I guess I could relate the thermal diffusivity to specific heat somehow, but the papers don't provide any temperature dependence so I think they won't help to answer my problem.

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  • $\begingroup$ Try this : google.com/url?sa=t&source=web&rct=j&url=http://… $\endgroup$
    – my2cts
    Commented May 5, 2019 at 11:51
  • $\begingroup$ that's the paper I cited in the question, experimental data is given only for graphite there, the graphene curve in the plot is only theoretical prediction $\endgroup$
    – Miriam K.
    Commented May 5, 2019 at 11:53
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    $\begingroup$ Oops then I guess the field is still wide open! $\endgroup$
    – my2cts
    Commented May 5, 2019 at 12:08

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