# Superconducting Gap in Superconductors

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.

• Please give a reference. – my2cts Aug 30 '19 at 18:53

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.