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

Abstract: We show that the momentum-dependent scaling exponents of the holographic fermion self-energy of the conformal-to-AdS$<em>2$ Gubser-Rocha model can describe new findings from angle-resolved photoemission spectroscopy experiments on a single layer (Pb,Bi)$</em>{2}$Sr$<em>{2-x}$La$_x$CuO$</em>{6+\delta}$ 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 $\Sigma&#39;&#39;_{\text{PLL}}(\omega) \propto (\omega<sup>2)<sup>\alpha$. 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 semi-holographic model that predicts a momentum-dependent scaling exponent in the electron self-energy as $$\Sigma(\omega,k) \propto \omega (-\omega^{2)^{\alpha} (1 - (k - k_F)/k_F) - 1/2}$$, with $\hbar k_F$ the Fermi momentum.