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

## TL;DR

This study uses machine learning to uncover hidden self-energy structures in cuprate superconductors, revealing their role in high-temperature superconductivity and demonstrating the potential of ML-based spectroscopy for fundamental insights.

## Contribution

The paper introduces a machine learning approach to extract hidden self-energies from experimental spectra, revealing their critical role in cuprate superconductivity, which was previously inaccessible.

## Key findings

- Peak structures in self-energies are linked to superconducting gaps.
- Hidden self-energy peaks cancel in total self-energy, making them invisible.
- Universal carrier relaxation correlates with high critical temperatures.

## Abstract

Experimental data are the source of understanding matter. However, measurable quantities are limited and theoretically important quantities are sometimes hidden. Nonetheless, recent progress of machine-learning techniques opens possibilities of exposing them only from available experimental data. In this paper, after establishing the reliability of the method in various careful benchmark tests, the Boltzmann-machine method is applied to the angle-resolved photoemission spectroscopy spectra of cuprate high temperature superconductors, Bi$_2$Sr$_2$CuO$_{6+\delta}$ (Bi2201) and Bi$_2$Sr$_2$CaCuO$_{8+\delta}$ (Bi2212). 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 universally dominant contributions to superconducting gap, hence evidencing the signal that generates the high-$T_{\rm c}$ superconductivity. The relation between superfluid density and critical temperature supports involvement of universal carrier relaxation associated with dissipative strange metals, where enhanced superconductivity is promoted by entangled quantum-soup nature of the cuprates. The present achievement opens avenues for innovative machine-learning spectroscopy method to reveal fundamental properties hidden in direct experimental accesses.