Electron tunneling measurements have proven enormously valuable in studies of conventional superconductors. Very early measurements confirmed, in an especially convincing way, the existence of the superconducting energy gap, and more detailed studies demonstrated the spectral form of the gap and its temperature dependence. These measurements were instrumental in confirming in some detail the predictions of the Bardeen, Cooper, Schrieffer (BCS) theory of superconductivity in simple metals. For example, it was shown very clearly that the ratio of the energy gap (2Δ) and critical temperature Tc was close to the BCS value (2Δ/kTc = 3.5). As the sophistication of the technique improved, deviations from this BCS weak coupling limit became apparent (2Δ/kTc was measured to be >4 in materials like Pb, for example), and subtle structure in the current-voltage characteristics of tunnel junctions unearthed a signature of the electron-phonon interaction—the microscopic mechanism responsible for superconductivity in these traditional materials. Through a quantitative analysis of this structure, people were able to extract a function α2(ω)F(ω), which is the phonon density of states F(ω) modulated by the electron-phonon coupling function α2(ω). This function gave a quantitative description of the electron-phonon interaction and confirmed beyond a doubt that the electron-phonon interaction was responsible for superconductivity.
Methods of solving the system of equations for the energy gap in the revisited BCS theory of superconductivity
