Thermal decoupling in high-$T_c$ cuprate superconductors

In unconventional high-$T_c$ cuprate superconductors, the intricate interplay between the non-ergodic bad metal and the strange metal state has remained enigmatic. Herein, we unravel this mystery using ab initio molecular dynamics simulations and the temperature-dependent effective potential method. Our investigation, centered on YBa$_2$Cu$_3$O$_7$ , provides the first simulation report on the $B_{1g}$ phonon anomaly, unveiling thermal decoupling induced by the bond weakening between the Ba atom and CuO$_2$ plane. This decoupling emerges as a pivotal underpinning behind several puzzling phenomena in high-$T_c$ superconductivity. Our results indicate that the effective temperature on the BaO plane deviates from that of the CuO$_2$ plane at low temperatures. Furthermore, we delineate the correlation between thermal decoupling and the Planckian dissipation, rigorously and quantitatively revealing a connection between linear-$T$ resistivity, Uemura relation, and superconducting domes, which are known to be the most important unsolved mysteries of high-$T_c$ superconductivity. The suppressed isotope effect ($\boldsymbol{\alpha}$ $\approx$ 0.02) in cuprates is also quantitatively explained from thermal decoupling. Our discoveries offer a revolutionary perspective on high-$T_c$ superconductivity, suggesting the potential for a transformative shift in our comprehension. Furthermore, they suggest that the autonomous emergence of low-temperature layers within materials has the potential to revolutionize industrial thermal management challenges.