Investigation of particle-hole asymmetry in the cuprates via electronic Raman scattering

In this paper we examine the effects of electron-hole asymmetry as a consequence of strong correlations on the electronic Raman scattering in the normal state of copper oxide high-temperature superconductors. Using determinant quantum Monte Carlo simulations of the single-band Hubbard model, we construct the electronic Raman response from single-particle Green's functions and explore the differences in the spectra for electron and hole doping away from half filling. The theoretical results are compared to new and existing Raman scattering experiments on hole-doped La${}_{2-x}$Sr${}_x$CuO${}_4$ and electron-doped Nd${}_{2-x}$Ce${}_x$CuO${}_4$. These findings suggest that the Hubbard model with fixed interaction strength qualitatively captures the doping and temperature dependence of the Raman spectra for both electron and hole doped systems, indicating that the Hubbard parameter $U$ does not need to be doping dependent to capture the essence of this asymmetry.

Figure 1

Theoretical band dispersion along high-symmetry directions for the single-band Hubbard model at half filling with parameters $t^{\prime }=-0.3t$, $\mu =0.0t$, $U=8.0t$, and $\beta =3.0/t$ obtained using determinant quantum Monte Carlo as described in the main text. The red (solid) arrows highlight possible $q=(0,0)$ transitions in the $B_{1g}$ Raman-scattering channel while the purple (dashed) arrows highlight possible transitions in the $B_{2g}$ channel along these high-symmetry cuts. Adapted from Ref. 35.

Figure 2

Theoretical band dispersion along high-symmetry directions for the single-band Hubbard model near optimal ($\sim$$15\%$) hole doping ($t^{\prime }=-0.3t$, $\mu =-2.5t$, $U=8.0t$, and $\beta =3.0/t$) with red (solid) and purple (dashed) arrows highlighting the prominent transitions in the Raman response in $B_{1g}$ and $B_{2g}$ channels, respectively.

Figure 3

Theoretical band dispersion along high-symmetry directions for the single-band Hubbard model near optimal ($\sim$$15\%$) electron doping ($t^{\prime }=-0.3t$, $\mu =2.0t$, $U=8.0t$, and $\beta =3.0/t$) with red (solid) and purple (dashed) arrows highlighting the prominent transitions in the $B_{1g}$ and $B_{2g}$ Raman response, respectively.

Figure 4

Theoretical Raman response in $B_{1g}$ (red, solid curve) and $B_{2g}$ (purple, dashed curve) symmetries for the half filled single-band Hubbard model (parameters as in Fig. 1).

Figure 5

Theoretical Raman response in the [(a) and (b)] $B_{1g}$ and [(c) and (d)] $B_{2g}$ channels for various doping levels on the [(a) and (c)] electron and [(b) and (d)] hole sides of the phase diagram for the single-band Hubbard model.

Figure 6

Theoretical low-energy Raman response in [(a) and (b)] $B_{1g}$ and [(c) and (d)] $B_{2g}$ symmetry from Fig. 5. These results have been converted to cm${}^{-1}$ assuming a reasonable value of $t=400$ meV that provides a qualitatively good description of the single-particle spectral function in these systems.

Figure 7

High-energy Raman response of (a),(b) NCCO and (c),(d) LSCO for electron and hole doping, respectively. The spectra are shown in [(a),(c)] $B_{1g}$ and [(b),(d)] $B_{2g}$ symmetry at various doping levels at temperatures of roughly 200 K. The peaks at low doping in (a) and (c) are due to two magnon scattering. In general with increasing doping level the spectra on the hole-doped side lose intensity while the intensity of the spectra on the electron-doped side increases. Part of the results are similar to those of other authors (Refs. 51, 52, 53 and 55) or were already published in Ref. 49.

Figure 8

Temperature dependence of the low-energy Raman response of overdoped (a) NCCO and (b) LSCO in $B_{2g}$ symmetry. Only for the electron-doped compound does there develop a quasiparticle peak at low temperatures. Results for NCCO with $x=0.15$ displaying similar properties were published in Ref. 63. The data for LSCO are adapted from Ref. 49.

Figure 9

Temperature dependence of the (a) and (b) experimental and (c) and (d) theoretical Raman resistivities in $B_{1g}$ (red) and $B_{2g}$ (purple) symmetry obtained from the electron- (Nd${}_{2-x}$Ce${}_x$CuO${}_4$) and hole-doped (La${}_{2-x}$Sr${}_x$CuO${}_4$) samples around optimal doping, respectively. The smooth black lines in (a) and (b) represent resistivity measured by transport in Ref. 47.

Figure 10

Ratio of the intensities in $I_{\mathrm{B}1\mathrm{g}}/I_{\mathrm{B}2\mathrm{g}}$ as extracted from the theoretical (upper) and experimental (lower) Raman spectra for electron- and hole-doping levels indicated in each panel.