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

Abstract

Photoemission spectroscopy on high $T_c$ superconductors find a puzzling nodal self-energy with $ω/T$ scaling and an exponent varying continuously with doping. We propose a mechanism: nonlocality induced by poorly screened effective repulsions $V_α(r) \sim 1/r^α$, where a continuously doping-dependent exponent $1 \le α\le 3$ interpolates between the Mott insulating and Fermi liquid limits. We develop a phenomenology of hydrodynamic screening, finding a scale-covariant quasiparticle decay rate $Γ(ω,T) \propto T^γ Φ(ω/T)$ in energy $ω$ and temperature $T$, with $γ= 2-\frac{1}α$ for nonlocal $ 1 < α< 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&#39;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 $ω/T$ scaling is experimentally observed.