Coherence gap edge and pseudo-gap in cuprates and other non-BCS superconductors

The energy gap Δ, proportional to the critical temperature, is the unique energy scale that characterizes the superconducting state in BCS theory. It is the single particle excitation energy Δ_p seen by tunneling experiments as well as the coherence gap edge Δ_c, up to which electron-hole reflections take place at clean superconducting/normal (S/N) interfaces, seen by point contacts. Both scales go to zero at the critical temperature Tc. These BCS predictions are well verified in conventional superconducting metals and alloys. But we show that they are violated in a variety of new superconductors such as the High Tc cuprates, granular Aluminum and other quasi two-dimensional compounds such as intercalated nitrides. In this new class of superconductors Δ_p is not anymore proportional to the critical temperature, while Δ_c is. Δ_p persists above Tc, Δ_c does not. Spectroscopic maps show that at energies larger than Δ_c the superconducting state becomes inhomogeneous, breaking up into nano-scale regions having different values of Δ_p. Coherence is lost, which explains why non-local electron-hole reflections are quenched.