Energy gaps and Kohn anomalies in elemental superconductors

The problem of conventional superconductivity has been considered solved since the Nobel-prize-winning work of Bardeen, Cooper, and Schrieffer (BCS) more than 50 years ago. But some well-established physical theories can turn out to be incomplete when they are checked by newly emerging experimental probes. Data derived from the triple-axis spin-echo (TRISP) method, which has enhanced the energy resolution of neutron spectroscopy by more than two orders of magnitude, present such a challenge to the BCS theory [1].

Lead and niobium are conventional elemental superconductors that are generally considered to follow the BCS theory (Fig. 1). Their normal state is characterized by a Fermi surface – a surface in the reciprocal space that separates occupied and unoccupied electronic states. When these metals enter the superconducting state at extremely low temperatures (just a few degrees above absolute zero), the so-called energy gap opens up all over the Fermi surface. The magnitude of this gap, however, is very hard to compute, because according to BCS it depends exponentially on materials-specific parameters such as the density of states at the Fermi surface and the electron-phonon coupling.

In experiments on the conventional elemental superconductors lead and niobium at our newly developed TRISP spectrometer, we have discovered a relationship between the superconducting energy gap and the geometry of the Fermi surface that had not been anticipated by the BCS theory. In every metal, one can find a certain set of wavevectors that connect diametrically opposite parts of the Fermi surface, which are known as nesting vectors. Due to the coupling of the electrons to lattice vibrations (phonons), the phonon lifetime is drastically reduced in the vicinity of such vectors, where more channels for electron scattering become available. These so-called Kohn anomalies in the phonon spectrum carry information about the fine details of the normal-state Fermi surface shape. Using the superior energy resolution of TRISP [2], we can now accurately determine the lifetimes of phonons in metals over the entire Brillouin zone [1,3,4]. Our data (Fig. 2) imply that the energy gap at low temperatures is determined entirely by the locus of the lowest-energy Kohn anomaly [1]. In other words, we can predict the low-temperature superconducting energy gap from the experimentally determined Kohn anomalies, without recourse to the BCS theory or other models of superconductivity. These results connect two phenomena that had previously been considered as unrelated, and they throw entirely new light on conventional superconductors that had long been thought to be completely understood.

Current TRISP experiments aim to establish the generality of these results in other superconducting elements and alloys, as well as the chemically more complex copper oxide and iron arsenide superconductors.