Energy Gaps and Kohn Anomalies in Elemental Superconductors

Experimental data on superconductors can be interpreted using a comprehensive framework based on the Bardeen-Cooper-Schrieffer formulation. Although the discovery of high-temperature superconductivity has challenged this framework, it remains effective in characterizing the physical properties of conventional low-temperature superconductors. However, the transition temperature and the energy gap at the Fermi level, which are two of the most important quantities associated with a superconductor, are still difficult to predict from first principles, because both depend exponentially on material-specific parameters such as the electronic and phononic densities of states and the electron-phonon coupling.
Using resonant spin-echo spectroscopy with neutrons, researchers examined the momentum and temperature dependence of the lifetimes of acoustic phonons in lead (Pb) and niobium (Nb). Lead and niobium are elements with the highest superconducting transition temperatures at 7.2 and 9.3 kelvin, respectively. Because electron-phonon scattering is suppressed for energies lower than the energy gap, the gap can be directly determined in phonon lifetime measurements. The superconducting energy gap in both lead and niobium converges with sharp Kohn anomalies originating from Fermi-surface nesting at low temperatures, implying an unexpected relation between the gap and the geometry of the Fermi surface. For phonon wave vectors connecting nearly parallel segments of the Fermi surface, the electron-phonon scattering probability is enhanced, and Kohn anomalies are often expected to occur. The detection of a low-temperature energy gap coinciding with Kohn anomalies in lead and niobium has not been anticipated by the standard theoretical framework for conventional superconductors.
The results indicate electron many-body correlations beyond the standard theoretical framework for conventional superconductivity. When the temperature is reduced, the spin-echo decay rate, which is proportional to the phonon linewidth and inversely proportional to its lifetime, decreases, indicating that the electron-phonon decay channel is lost in the superconducting state. Dynamical nesting of the Fermi surface is possibly induced by the interplay between superconductivity and spin- or charge-density wave fluctuations.