Superconductivity is the property of certain materials to conduct electricity with no energy losses when cooled below a critical temperature. The discovery of high-temperature copper oxide (or cuprate) superconductors, whose critical temperatures reach about 160 K, has unlocked various potential applications.

However, the mechanisms driving the high-temperature superconductivity are not fully understood, primarily due to challenges in dealing with the electron–electron interactions within the materials. Spectroscopic experiments and nonperturbative theories have been used to explain the high-temperature superconductivity in cuprates.

Recently, in a new study published in the Journal of the Physical Society of Japan , researcher Shiro Sakai from the Center for Emergent Matter Science at RIKEN, Japan, reviewed the results of these studies, highlighting that superconductivity in cuprates can be explained by the existence of a self-energy singularity.

The singular self-energy, described as a nonperturbative effect, arises from strong correlations between electrons. Referred to as the ‘missing link,’ the self-energy singularity offers a unifying explanation for the various phases observed in cuprates as well as for a number of experimental observations that have been considered ‘anomalies’ and remain poorly understood.

Cuprates exhibit superconductive properties only within a doping range of 5–25%. At lower doping, hole-doped cuprates behave as Mott insulators, while at higher doping, they show a Fermi-liquid behavior. Additionally, in the underdoped regions lying above the critical temperature, an enigmatic pseudogap state emerges.

It is known that the singular self-energy exists in the Mott insulating state, where it generates a spectral gap. On top of that, nonperturbative calculations have revealed its presence in the finite-doping region as well, where it enhances the superconductivity transition temperature and generates the pseudogap above it.

Therefore, the self-energy singularity is at the origin of the high-temperature superconductivity, the pseudogap, and the Mott insulator phases in cuprates. This review thus sheds light on the complex nature of cuprates, paving the way for the design and discovery of new superconductors with higher critical temperatures.