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

Photoemission spectroscopy on high $T_c$ superconductors find a puzzling nodal self-energy with $\omega \mathrm{/}T$ scaling and an exponent varying continuously with doping. We propose a mechanism: nonlocality induced by poorly screened effective repulsions $V_{\alpha }(r)\sim 1\mathrm{/}{r}^{\alpha }$, 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 $\mathrm{\Gamma }(\omega ,T)\propto T^{\gamma }\mathrm{\Phi }(\omega \mathrm{/}T)$ 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 $\omega \mathrm{/}T$ scaling is experimentally observed.