We show that the momentum-dependent scaling exponents of the holographic fermion self-energy of the conformal-to-AdS
2 Gubser-Rocha model can describe new findings from angle-resolved photoemission spectroscopy experiments on a single layer (Pb,Bi)
2Sr
2−xLa
xCuO
6+δ 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
ΣPLL′′(ω)∝(ω2)α. 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
Σ(ω,k)∝ω(−ω2)α(1−(k−kF)/kF)−1/2, with
ℏkF the Fermi momentum.
We show that the momentum-dependent scaling exponents of the holographic fermion self-energy of the conformal-to-
AdS2 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.
A bstract Semi-holography, originally proposed as a model for conducting lattice electrons coupled to a holographic critical sector, leads to an effective theory of non-Fermi liquids with only a few relevant interactions on the Fermi surface in the large N limit. A refined version of such theories has only two effective couplings, which give holographic and Fermi-liquid-like contributions to the self-energy, respectively. We show that a low co-dimension sub-manifold exists in the space of refined semi-holographic theories in which strange metallic behavior is manifested and which can be obtained just by tuning the ratio of the two couplings. On this sub-manifold, the product of the spectral function and the temperature is approximately independent of the critical exponent, the Fermi energy, and the temperature at all frequencies and near the Fermi surface when expressed in terms of suitably scaled momentum and frequency variables. This quasi-universal behavior leads to linear-in- T dc resistivity and Planckian dissipation over a large range of temperatures, and we also obtain T −3 scaling of the Hall conductivity at higher temperatures. The quasi-universal spectral function also fits well with photoemission spectroscopic data without varying the critical exponent with the doping. Combining with the results for optical conductivity, we construct a generalized version of Drude phenomenology for strange-metallic behavior, which satisfies non-trivial consistency tests. Finally, we discuss a possible dynamical mechanism for the fine-tuning of the ratio of the two couplings necessary to realize the strange metallic behavior in a typical state.
The strange metal is an enigma within the field of many-body quantum physics, as it defies the standard Fermi liquid theory of metals due to the absence of well-defined, electron-like quasiparticles. It has been presumed that strange metal behavior arises due to strong correlations between electrons that are not present in ordinary Fermi liquids, but the exact nature of these correlations is unknown. To this end, this thesis aims to address the fundamental question: What, precisely, is so strongly correlated about charge in the strange metal? This question is tackled by experimentally measuring the dynamic charge response function, which directly encodes charge correlations in momentum and energy, using the technique of Momentum-resolved Electron Energy-loss Spectroscopy (M-EELS). In particular, two prototypical members of the cuprate and ruthenate strange metal families are studied: Bi-2212 and Sr
2RuO
4. By studying Bi-2212 at optimal doping, it is found that the charge response of the strange metal is characterized by a broad continuum of fluctuations that are momentum and energy independent over a large range of parameter space, unlike Fermi liquid charge correlations which exhibit propagating density waves of charge with well defined energy and momentum (i.e. plasmons). We argue that, in essence, the charge correlations of the strange metal are highly localized in both space and time, unlike the Fermi Liquid where they are localized in momentum and energy instead. To understand how charge correlations change as one leaves the strange metal regime, the M-EELS response of Bi-2212 is mapped out as a function of doping and temperature. At high temperature, it is found that the continuum is largely doping independent. However, upon cooling, very large changes in spectral weight are observed over a range of energy scales nearly two orders of magnitude larger than the thermal scale
kBT. Moreover, this change in spectral weight undergoes a sign reversal as a function of doping, with spectral weight enhancement on the underdoped side, suppression in the overdoped regime, and no change at optimal doping. These changes in spectral weight are completely unlike the case of the Fermi liquid, where doping only acts to rigidly shift the plasmon energy and no significant changes occur as a function of temperature. Finally, we venture further and ask whether strange metal and Fermi liquid charge correlations can simultaneously coexist in a material. To explore this possibility, we measured the M-EELS response of Sr
2RuO
4, a material which exhibits strange and bad metal behavior at high temperature, but transitions to a well-defined Fermi liquid at low temperature. Surprisingly, in the strange metal regime, Sr
2RuO
4 exhibits both a broad continuum similar to Bi-2212 and a propagating Fermi liquid collective mode at low-energies and momentum. Upon cooling, low-energy spectral weight is suppressed in the strange metal continuum and the Fermi liquid collective mode velocity is strongly renormalized. These findings confirm the strange metal and Fermi liquid can coexist and demonstrate that Sr
2RuO
4 exhibits charge correlations with strange metal character at high energies and short length scales and Fermi liquid character at low energies and long wavelengths.
We develop a Neural-ODE framework to infer effective bulk metric functions and the charge-weighted gauge potential from boundary fermionic spectra within a static, planar black-hole ansatz. Controlled benchmarks recover the known bulk profiles of the Einstein--Maxwell and Gubser--Rocha models. We then use normalized interaction self-energy targets generated from an extended power-law liquid model with parameters calibrated by angle-resolved photoemission measurements to test the proposed geometric explanation of cuprate strange-metal spectra in a semi-holographic setting. For this application, we use a massless probe in backgrounds with conformal-to-
AdS2×R2 asymptotics and derive a spectral extraction formula from the conserved radial Dirac flux. We identify coordinate/Weyl redundancy and a degeneracy in the scaled Hawking temperature of the normalized inverse problem. The conformal factor remains undetermined, so bulk entropy and the associated contribution to electronic specific heat require independent input. Low-temperature targets are fitted accurately across the studied doping range. In the high-temperature test, however, the present ansatz and optimization search have not yielded a refined geometry that accurately reproduces the thermal spectral shape while preserving frequency symmetry. These results may guide the further development of semi-holographic models for cuprates, and the framework may also find applications in other strongly correlated electron systems.
A refined semi-holographic non-Fermi liquid model, in which carrier electrons hybridize with operators of a holographic critical sector, has been proposed recently for strange metallic behavior. The model, consistently with effective theory approach, has two couplings whose ratio is related to the doping. We explain the origin of the linear-in-T resistivity and strange metallic behavior as a consequence of the emergence of a universal form of the spectral function which is independent of the model parameters when the ratio of the two couplings take optimal values determined only by the critical exponent. This universal form fits well with photoemission data of copper oxide samples for under/optimal/over-doping with a fixed exponent over a wide range of temperatures. We further obtain a refined Planckian dissipation scenario in which the scattering time
τ=f⋅ℏ/(kBT), with
f being
O(1) at strong coupling, but
O(10) at weak coupling.