Study of Spin and Charge Fluctuations in the U-t-t' Model

TL;DR

This study demonstrates that a single Hubbard U-t-$t'$ model with fixed parameters can accurately reproduce magnetic and electronic properties of high-temperature superconductors LSCO and YBCO, highlighting the role of Fermi surface shape.

Contribution

It shows that a unified one-band Hubbard model with specific parameters explains experimental observations for different cuprates, challenging previous multi-parameter models.

Findings

Good agreement between model calculations and neutron scattering data.

Fermi surface shape influences incommensuration tendencies.

More negative $t'/t$ induces diagonal incommensuration, conflicting with experiments.

Abstract

As additional neutron scattering experiments are performed on a variety of high temperature superconducting compounds it appears that magnetic incommensuration is a phenomenon common to all of the samples studied. The newest experimental results indicate that incommensurate peaks exist at momentum ${\bf q}=\pi(1,1\pm\delta)$ and $\pi(1\pm\delta,1)$ in $La_{2-x}Sr_xCuO_4}$ (LSCO) and ${\rm YBa_2Cu_3O_{7-\delta}}$ (YBCO). The dependence of $\delta$ with hole doping appears to be similar in both materials. In addition, new ARPES data for LSCO as a function of doping show that its Fermi surface is qualitatively similar to the one of YBCO, contrary to what was previously believed. Early theoretical attempts to explain LSCO and YBCO behavior usually relied on one- or three-band Hubbard models or the t-J model with electron hopping beyond nearest-neighbor and with different parameter values for each material. In this paper it is shown that using a one band Hubbard U-t-$t'$ model with a unique set of parameters, U/t=6 and $t'$/t=-0.25, good agreement is obtained between computational calculations and neutron scattering and ARPES experiments for LSCO and YBCO. It is also shown that using a more negative $t'$/t will induce short-range magnetic incommensuration along the diagonal direction in the Brillouin zone, in qualitative disagreement with the experimental results. At the finite temperatures of the present Monte Carlo simulation it is also observed that in this model the tendency to incommensuration appears to be more related to the shape of the two-dimensional Fermi surface and the strength of the interaction, rather than to charge order.