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arXiv:1106.5798 · Physical Review B

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

Brian Moritz, Steven Johnston, Thomas Devereaux, B. Muschler, W. Prestel, R. Hackl, Michael Lambacher, Andreas Erb, Seiki Komiya, Yoichi Ando

Published Dec 5, 2011• 16 citations
arXivHTMLPDF

Abstract

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${}_{2\ensuremath{-}x}$Sr${}_{x}$CuO${}_{4}$ and electron-doped Nd${}_{2\ensuremath{-}x}$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.

DOI
10.1103/physrevb.84.235114

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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 La2\ensuremath−x{}_{2\ensuremath{-}x}2\ensuremath−x​Srx{}_{x}x​CuO4{}_{4}4​ and electron-doped Nd2\ensuremath−x{}_{2\ensuremath{-}x}2\ensuremath−x​Cex{}_{x}x​CuO4{}_{4}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 UUU does not need to be doping dependent to capture the essence of this asymmetry.
Recent experiments revealed a striking asymmetry in the phase diagram of the high temperature cuprate superconductors. The correlation effect seems strong in the hole-doped systems and weak in the electron-doped systems. On the other hand, a recent theoretical study shows that the interaction strengths (the Hubbard U) are comparable in these systems. Therefore, it is difficult to explain this asymmetry by their interaction strengths. Given this background, we analyze the one-particle spectrum of a single band model of a cuprate superconductor near the Fermi level using the dynamical mean field theory. We find the difference in the "visibility" of the strong correlation effect between the hole- and electron-doped systems. This can explain the electron-hole asymmetry of the correlation strength without introducing the difference in the interaction strength.
We carry out a systematic study of collective spin and charge excitations for the canonical single-band Hubbard, t–J–U, and t–J models of high-temperature copper-oxide superconductors, both on electron- and hole-doped side of the phase diagram. A~recently developed variational wave function approach, combined with the expansion in the inverse number of fermionic flavors, is employed. All three models exhibit a substantial electron–hole asymmetry of magnetic excitations, with a robust paramagnon emerging for hole-doping, in agreement with available resonant inelastic X-ray scattering data for the cuprates. The t–J model yields additional high-energy peak in the magnetic spectrum that is not unambiguously identified in spectroscopy. For all considered Hamiltonians, the dynamical charge susceptibility contains a coherent mode for both hole- and electron doping, with overall bandwidth renormalization controlled by the on-site Coulomb repulsion. Away from the strong-coupling limit, the antiferromagnetic ordering tendency is more pronounced on the electron-doped side of the phase diagram.
To shed light on how electronic correlations vary across the phase diagram of the cuprate superconductors, we examine the doping evolution of spin and charge excitations in the single-band Hubbard model using determinant quantum Monte Carlo (DQMC). In the single-particle response, we observe that the effects of correlations weaken rapidly with doping, such that one may expect the random phase approximation (RPA) to provide an adequate description of the two-particle response. In contrast, when compared to RPA, we find that significant residual correlations in the two-particle excitations persist up to 40% hole and 15% electron doping (the range of dopings achieved in the cuprates). These fundamental differences between the doping evolution of single- and multiparticle renormalizations show that conclusions drawn from single-particle processes cannot necessarily be applied to multiparticle excitations. Eventually, the system smoothly transitions via a momentum-dependent crossover into a weakly correlated metallic state where the spin and charge excitation spectra exhibit similar behavior and where RPA provides an adequate description.
The pseudogap regime of the cuprate high-temperature superconductors is characterized by a variety of competing orders, the nature of which are still widely debated. Recent experiments have provided evidence for electron nematic order, in which the electron fluid breaks rotational symmetry while preserving translational invariance. Raman spectroscopy, with its ability to symmetry resolve low energy excitations, is a unique tool that can be used to assess nematic fluctuations and nematic ordering tendencies. Here we compare results from determinant quantum Monte Carlo simulations of the Hubbard model to experimental results from Raman spectroscopy in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$, which show a prominent increase in the B1g{B}_{1g}B1g​ response around 10% hole doping as the temperature decreases, indicative of a rise in nematic fluctuations at low energy. Our results support a picture of nematic fluctuations with B1g{B}_{1g}B1g​ symmetry occurring in underdoped cuprates, which may arise from melted stripes at elevated temperatures.
The competition between ddd-wave superconductivity (SC) and antiferromagnetism (AF) in the high-Tc{T}_{c}Tc​ cuprates is investigated by studying the hole- and electron-doped two-dimensional Hubbard model with a recently proposed variational quantum-cluster theory. The approach is shown to provide a thermodynamically consistent determination of the particle number, provided that an overall shift of the on-site energies is treated as a variational parameter. The consequences for the single-particle excitation spectra and for the phase diagram are explored. By comparing the single-particle spectra with quantum Monte Carlo and experimental data, we verify that the low-energy excitations in a strongly correlated electronic system are described appropriately. The cluster calculations also reproduce the overall ground-state phase diagram of the high-temperature superconductors. In particular, they include salient features such as the enhanced robustness of the antiferromagnetic state as a function of electron doping and the tendency towards phase separation into a mixed antiferromagnetic-superconducting phase at low doping and a pure superconducting phase at high (both hole and electron) doping.
There is growing evidence that the hole-doped single-band Hubbard and t - J models do not have a superconducting ground state reflective of the high-temperature cuprate superconductors but instead have striped spin- and charge-ordered ground states. Nevertheless, it is proposed that these models may still provide an effective low-energy model for electron-doped materials. Here we study the finite temperature spin and charge correlations in the electron-doped Hubbard model using quantum Monte Carlo dynamical cluster approximation calculations and contrast their behavior with those found on the hole-doped side of the phase diagram. We find evidence for a charge modulation with both checkerboard and unidirectional components decoupled from any spin-density modulations. These correlations are inconsistent with a weak-coupling description based on Fermi surface nesting, and their doping dependence agrees qualitatively with resonant inelastic x-ray scattering measurements. Our results provide evidence that the single-band Hubbard model describes the electron-doped cuprates.