Energy-length scaling of critical phase fluctuations in the cuprate pseudogap phase

Abstract

The quantum origin of the cuprate pseudogap and its relationship to symmetry-breaking orders is a central conundrum of unconventional superconductors. The difficulty is deeply rooted in modeling simultaneous organizations in multiple degrees of freedom (including spin, momentum, and real space) generated by strong electron-electron correlations. Beyond early theories focusing on the description in spin and momentum space, recent studies turn to examine the spatial organization and intertwining mechanism of multiple orders. In this review, we summarize some progress in understanding the spatial organization of critical fluctuations and highlight the recent discovery of a universal energy-length scaling. This scaling quantitatively explains the nontrivial magnitude and doping dependence of the pseudogap energy and critical temperature and their relations to charge and superconducting ordering. We close with a prospect of the spatial organization mechanism of intertwined orders and its possible composite energy scaling.