Gauge-gravity duality comes to the laboratory: Evidence of momentum-dependent scaling exponents in the nodal electron self-energy of cuprate strange metals

We show that the momentum-dependent scaling exponents of the holographic fermion self-energy of the conformal-to-${\mathrm{AdS}}₂$ Gubser-Rocha model can describe new findings from angle-resolved photoemission spectroscopy experiments on a single-layer (Pb,Bi)${}₂{\mathrm{Sr}}_{2\ensuremath{-}x}{\mathrm{La}}_x{\mathrm{CuO}}_{6+\ensuremath{\delta}}$ copper oxide. In particular, it was recently observed in high-precision measurements on constant energy cuts along the nodal direction that the spectral function departs from the Lorentzian line shape that is expected from the power-law-liquid model of a nodal self-energy, with an imaginary part featureless in momentum as ${\mathrm{\ensuremath{\Sigma}}}_{\text{PLL}}^{\ensuremath{'}\ensuremath{'}}(\ensuremath{\omega})\ensuremath{\propto}{({\ensuremath{\omega}}²)}^{\ensuremath{\alpha}}$. By direct comparison with experimental results, we provide evidence that this departure from either a Fermi liquid or the power-law liquid, resulting in an asymmetry of the spectral function as a function of momentum around the central peak, is captured at low temperature and all dopings by a semiholographic model that predicts a momentum-dependent scaling exponent in the electron self-energy as $\mathrm{\ensuremath{\Sigma}}(\ensuremath{\omega},k)\ensuremath{\propto}\ensuremath{\omega}{(\ensuremath{-}{\ensuremath{\omega}}²)}^{\ensuremath{\alpha}(1\ensuremath{-}(k\ensuremath{-}{k}_F)/{k}_F)\ensuremath{-}1/2}$, with $\ensuremath{\hbar}{k}_F$ the Fermi momentum.