Coexisting pseudogap, charge-transfer-gap, and Mott-gap energy scales in the resonant inelastic x-ray scattering spectra of electron-doped cuprate superconductors

We present a computation of Cu $K$-edge resonant inelastic x-ray scattering (RIXS) spectra for electron-doped cuprates, which includes coupling to bosonic fluctuations. Comparison with experiment over a wide range of energy and momentum transfers allows us to identify the signatures of three key normal-state energy scales: the pseudogap, charge-transfer gap, and Mott gap. The calculations involve a three-band Hubbard Hamiltonian based on Cu $d_{x^2-y^2}$ and O $p_x$, $p_y$ orbitals, with a self-energy correction which arises due to spin and charge fluctuations. Our theory reproduces characteristic features, e.g., gap collapse, large spectral weight broadening, and spectral weight transfer as a function of doping, as seen in experiments.

Figure 1

(a) Spectral weight of electronic states in NCCO for $x=0.14$. A constant imaginary part of magnitude $0.5$ eV is added to broaden the spectra. (b) Calculated self-energy for antibonding bands. The red dashed curve and the blue solid curve are real and imaginary parts of the self-energy, respectively. (c) Spectral weight as in (a), but modified by the self-energy of (b).

Figure 2

RIXS spectra from NCCO for $x=0$: (a) theory without and (b) with self-energy corrections, and (c) experiment (Ref.14). (d)–(f) Similar figures for $x=0.14$.

Figure 3

RIXS spectra from NCCO for $x=0.075$, (a) experiment (Ref.28) and (b) theory. Intensity cuts along $\Gamma$, (c) for $x=0.075$ and (d) for $x=0$ with RIXS theory (blue solid line), RIXS experiment (red dot-dashed line), and optical experiment (green dashed line). In frames (a) and (b), solid arrows indicate intensity peaks along $\Gamma$, while dashed arrows indicate cuts taken in frame (c). In frames (c) and (d), the theoretical curves have been convoluted with a Gaussian broadening of 200 meV to mimic experimental resolution.

Figure 4

Comparison of theoretical (blue solid line) and experimental (red dashed line) spectra at half filling with $q$ fixed at (a): ($\pi ,0$), (b): $\Gamma$, (c): ($\pi /2,0$), and (d): ($\pi /2,\pi /2$). Panel (b) displays the high-energy RIXS peak from Ref.2. The theoretical curves have been convoluted with a Gaussian broadening of 200 meV to mimic experimental resolution.