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arXiv:1601.08249 · Physical review. B./Physical review. B

Plasmon excitations in layered high- T c cuprates

A. Greco, Hiroyuki Yamase, Matías Bejas

Published Aug 17, 2016• 45 citations
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Abstract

Motivated by the recent resonant inelastic x-ray scattering (RIXS) experiment for the electron-doped cuprates ${\mathrm{Nd}}_{2\ensuremath{-}x}{\mathrm{Ce}}_{x}{\mathrm{CuO}}_{4}$ with $x\ensuremath{\approx}0.15$, we compute the density-density correlation function in the $t\ensuremath{-}J$ model on a square lattice by including interlayer hopping and the long-range Coulomb interaction. We find that collective charge excitations are realized not inside the particle-hole continuum, but above the continuum as plasmons. The plasmon mode has a rather flat dispersion near the in-plane momentum ${\mathbf{q}}_{\ensuremath{\parallel}}=(0,0)$ with a typical excitation energy of the order of the intralayer hopping $t$ when the out-of-plane momentum ${q}_{z}$ is zero. However, when ${q}_{z}$ becomes finite, the plasmon dispersion changes drastically near ${\mathbf{q}}_{\ensuremath{\parallel}}=(0,0)$, leading to a strong dispersive feature with an excitation gap scaled by the interlayer hopping ${t}_{z}$. We discuss the mode recently observed by RIXS near ${\mathbf{q}}_{\ensuremath{\parallel}}=(0,0)$ in terms of the plasmon mode with a finite ${q}_{z}$.

DOI
10.1103/physrevb.94.075139

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Motivated by the recent resonant x-ray scattering (RXS) and resonant inelastic x-ray scattering (RIXS) experiments for electron-doped cuprates, we study the charge excitation spectrum in a layered $t\text{\ensuremath{-}}J$ model with the long-range Coulomb interaction. We show that the spectrum is not dominated by a specific type of charge excitations, but by different kinds of charge fluctuations, and is characterized by a dual structure in the energy space. Low-energy charge excitations correspond to various types of bond-charge fluctuations driven by the exchange term (JJJ term), whereas high-energy charge excitations are due to usual on-site charge fluctuations and correspond to plasmon excitations above the particle-hole continuum. The interlayer coupling, which is frequently neglected in many theoretical studies, is particularly important to the high-energy charge excitations.
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In this article, we discuss the nontrivial collective charge excitations (plasmons) of the extended square lattice Hubbard model. Using a fully nonperturbative approach, we employ the hybrid Monte Carlo algorithm to simulate the system at half-filling. A modified Backus-Gilbert method is introduced to obtain the spectral functions via numerical analytic continuation. We directly compute the single-particle density of states which demonstrates the formation of Hubbard bands in the strongly correlated phase. The momentum-resolved charge susceptibility also is computed on the basis of the Euclidean charge-density-density correlator. In agreement with previous extended dynamical mean-field theory studies, we find that, at high strength of the electron-electron interaction, the plasmon dispersion develops two branches.
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.