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arXiv:2004.08435 · Physical review. B./Physical review. B

Spectroscopic signatures of next-nearest-neighbor hopping in the charge and spin dynamics of doped one-dimensional antiferromagnets

Umesh Kumar, Alberto Nocera, Gregory Price, Kenneth Stiwinter, Steven Johnston, Trinanjan Datta

Published Aug 24, 2020• 14 citations
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Abstract

We study the impact of next-nearest-neighbor (NNN) hopping on the low-energy collective excitations of strongly correlated doped antiferromagnetic cuprate spin chains. Specifically, we use exact diagonalization and the density matrix renormalization group method to study the single-particle spectral function, the dynamical spin and charge structure factors, and the Cu $L$-edge resonant inelastic x-ray scattering (RIXS) intensity of the doped $t\text{\ensuremath{-}}t\ensuremath{'}\text{\ensuremath{-}}J$ model for a set of $t\ensuremath{'}$ values. We find evidence that the spin and charge degrees of freedom of the doped holes are not strictly separated anymore as $|t\ensuremath{'}|$ increases and identify the consequences of this in the dynamical response functions. The inclusion of NNN hopping couples the spinon and holon excitations, resulting in the formation of a spin polaron, where a ferromagnetic spin-polarization cloud dresses the doped carrier. The spin polaron manifests itself as additional spectral weight in the dynamical correlation functions, which appear simultaneously in the spin- and charge-sensitive channels. We also demonstrate that RIXS can provide a unique view of the spin polaron, due to its sensitivity to both the spin and charge degrees of freedom.

DOI
10.1103/physrevb.102.075134

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Holes doped within the square CuO2\mathrm{Cu}{\mathrm{O}}_{2}CuO2​ network specific to the cuprate superconducting materials have oxygen 2p2p2p character. We investigate the basic properties of such oxygen holes by wave-function-based quantum chemical calculations on large embedded clusters. We find that a 2p2p2p hole induces ferromagnetic correlations among the nearest-neighbor Cu3d\mathrm{Cu}\phantom{\rule{0.2em}{0ex}}3dCu3d spins. When moving through the antiferromagnetic background, the hole must bring along this spin-polarization cloud at nearby Cu sites, which gives rise to a substantial reduction of the effective hopping parameters. Such interactions can explain the relatively low values inferred for the effective hoppings by fitting the angle-resolved photoemission data. The effect of the background antiferromagnetic couplings of renormalizing the effective nearest-neighbor hopping is also confirmed by density-matrix renormalization-group model-Hamiltonian calculations for chains and ladders of CuO4\mathrm{Cu}{\mathrm{O}}_{4}CuO4​ plaquettes.
In a t-J model on a chain, an additional next-nearest-neighbor hopping term destroys the complete spin-charge separation at J/t\ensuremath{\ll}1 and induces the formation of stable spin-polarized S>0 states. The properties of a single ferromagnetic polaron are investigated by the exact diagonalization of small systems and by the approximative treatment of an effective model, describing a spinless fermion coupled to the spin background. Both methods give consistent results on the critical Jc{\mathit{J}}_{\mathit{c}}Jc​ for the polaron formation on the increase of the spin S and the polaron size with decreasing J. A very large enhancement of the polaron mass with increasing S is observed. Systems with a finite concentration of holes are also studied within the same framework. Analytical considerations indicate on the bound many-hole states and consequently on phase-separated regions in the phase diagram.
We calculate spin and charge excitation spectra of the one-dimensional (1D) quarter-filled Hubbard model with nearest-neighbor ttt and next-nearest-neighbor ${t}^{\ensuremath{'}}$ hopping integrals using the dynamical density-matrix renormalization group technique. We consider a case where ttt (>0)(>0)(>0) is much smaller than ${t}^{\ensuremath{'}}$ (>0)(>0)(>0). First, we examine the accuracy of our method based on comparison between our result and exact noninteracting spectrum. Next, we investigate the spectra with the on-site Coulomb interaction. We find that the spin and charge excitation spectra are essentially the same as those of the 1D quarter-filled Hubbard (and $t\text{\ensuremath{-}}J$) model for the two 1D chains along the hopping integral ${t}^{\ensuremath{'}}$. However, the hopping integral ttt $(<{t}^{\ensuremath{'}})$ plays a crucial role in the short-range correlations and low-energy excitaions; ferromagnetic correlation between electrons on neighboring sites is enhanced and pairing correlation between the electrons is induced. Consequently, a spin-triplet superconducting state may be derived.
We present a nonperturbative, divergence-free series expansion of Green's functions using effective operators. The method is especially suited for computing correlators of complex operators as a series of correlation functions of simpler forms. We apply the method to study low-energy excitations in resonant inelastic x-ray scattering (RIXS) in doped one- and two-dimensional single-band Hubbard models. The RIXS operator is expanded into polynomials of spin, density, and current operators weighted by fundamental x-ray spectral functions. These operators couple to different polarization channels resulting in simple selection rules. The incident photon energy dependent coefficients help to pinpoint main RIXS contributions from different degrees of freedom. We show in particular that, with parameters pertaining to cuprate superconductors, local spin excitation dominates the RIXS spectral weight over a wide doping range in the cross-polarization channel.