Hidden self-energies as origin of cuprate superconductivity revealed by machine learning.

Experimental data are the source of understanding matter. However, measurable quantities are limited and theoretically important quantities are often hidden. Nonetheless, recent progress of machine-learning techniques opens possibilities of exposing them only from available experimental data. In this article, the Boltzmann-machine method is applied to the angle-resolved photoemission spectroscopy spectra of cuprate superconductors. We find prominent peak structures both in normal and anomalous self-energies, but they cancel in the total self-energy making the structure apparently invisible, while the peaks make dominant contributions to superconducting gap, hence providing a decisive testimony for the origin of superconductivity. The relation between superfluid density and critical temperature supports involvement of universal carrier relaxation time associated with dissipative strange metals. The present achievement opens avenues for innovative machine-learning spectroscopy method.