Nonlocality can generate $\omega/T$ scaling without criticality in high $T_c$ strange metals

Abstract

Photoemission spectroscopy on high $T_c$ superconductors find a puzzling nodal self-energy with $\omega/T$ scaling and an exponent varying continuously with doping. We propose a mechanism: nonlocality induced by poorly screened effective repulsions $V_{\alpha}(r) \sim 1/r^\alpha$, where a continuously doping-dependent exponent $1 \le \alpha \le 3$ interpolates between the Mott insulating and Fermi liquid limits. We develop a phenomenology of hydrodynamic screening, finding a scale-covariant quasiparticle decay rate $\Gamma(\omega,T) \propto T^{\gamma} \Phi(\omega/T)$ in energy $\omega$ and temperature $T$, with $\gamma = 2-\frac{1}{\alpha}$ for nonlocal $ 1 < \alpha < 2$. Our results naturally capture the optimally doped to overdoped regimes, whereas the underdoped regime is qualitatively distinct. In our theory, spectroscopy-fitted exponents directly probe the charged fluid's effective spatial nonlocality, providing a way to falsify the theory by comparing photoemission spectroscopy against electron energy loss spectroscopy. More broadly, nonlocality cautions us to not immediately infer quantum critical phenomena when $\omega/T$ scaling is experimentally observed.