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An exact transition-temperature ( T c ) formula is derived within the van Hove scenario of BCS phonon-mediated pairing theory consisting of a logarithmic singularity in the density of states (DOS) at the Fermi energy. Also evaluated are a near-exact zero-temperature gap-energy expression along with an exact (numerical) temperature-dependent gap energy. Though T c is greatly enhanced over the conventional BCS (constant DOS) value for given (weak) coupling, the zero-temperature gap-to- T c ratio and the temperature-dependent gap energy both differ little from the BCS values.
Physical Review B – American Physical Society (APS)
Published: Jul 1, 1993
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