Momentum-dependent scaling exponents of nodal self-energies measured in strange metal cuprates and modelled using semi-holography

The anomalous strange metal phase found in high-$T_c$ cuprates does not follow the conventional condensed-matter principles enshrined in the Fermi liquid and presents a great challenge for theory. Highly precise experimental determination of the electronic self-energy can provide a test bed for theoretical models of strange metals, and angle-resolved photoemission can provide this as a function of frequency, momentum, temperature and doping. Here we show that constant energy cuts through the nodal spectral function in (Pb,Bi)$_{2}$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$ have a non-Lorentzian lineshape, meaning the nodal self-energy is $k$ dependent. We show that the experimental data are captured remarkably well by a power law with a $k$-dependent scaling exponent smoothly evolving with doping, a description that emerges naturally from AdS/CFT-based semi-holography. This puts a spotlight on holographic methods for the quantitative modelling of strongly interacting quantum materials like the cuprate strange metals.