Understanding BCS Theory

Abstract

New calculation reveals that E is constant in a thin layer across the Fermi surface, befitting the definition of energy gap parameter, Delta varies dramatically. The BCS self-consistent equation has a simple and exact solution, showing that the well-known ratio 3.5 must be replaced by 4. A simple formula is found to estimate energy gap from first principles with reasonable accuracy, useful to the current research into high Tc superconductivity.