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Please explain "Exponential behavior usually signals the presence of a gap in the energy spectrum" How The presence of a gap explains the exponential decrease of the specific heat and the thermal conductivity below TC.

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  • $\begingroup$ Please give a reference. $\endgroup$ – my2cts Aug 30 '19 at 18:53
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At low temperature number of excited electrons above the gap will be proportional to $\exp\{-\Delta/kT\}$ where $\Delta$ is the gap. This decreases very rapidly as $T$ becomes small so will be far fewer excitation than without the gap. Consequently the electronic contribution to the specific heat will be $\exp\{-\Delta/kT\}$ smaller. Gapless superconductors, on the other hand, have specific heats that go to zero as $T^a$ for some power $a$ that depends on the dimension (line or point) of the gapless region on the Fermi surface.

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