Checkerboard and stripe inhomogeneities in cuprates

TL;DR

This study explores charge-ordering phases in cuprates using a Gutzwiller approximation, revealing that stripe or checkerboard patterns dominate depending on the hopping parameters, with checkerboards favored at surfaces and a fixed periodicity.

Contribution

It demonstrates how the ratio of next-nearest to nearest neighbor hopping influences the emergence of stripe or checkerboard charge orders in cuprates.

Findings

Stripes occur when |t'/t| is small, typical for La2-xSrxCuO4.

Checkerboard structures are favored at larger |t'/t|, as in Ca2-xNaxCuO2Cl2 and Bi2Sr2CaCu2O8+δ.

Checkerboard charge periodicity remains locked at 4 units over a wide doping range.

Abstract

We systematically investigate charge-ordering phases by means of a restricted and unrestricted Gutzwiller approximation to the single-band Hubbard model with nearest ($t$) and next-nearest neighbor hopping ($t'$). When $|t'/t|$ is small, as appropriate for ${\rm La_{2-x}Sr_xCuO_4}$, stripes are found, whereas in compounds with larger $|t'/t|$ (such as ${\rm Ca_{2-x}Na_x CuO_2Cl_2}$ and ${\rm Bi_2Sr_2CaCu_2O_{8+\delta}}$) checkerboard structures are favored. In contrast to the linear doping dependence found for stripes the charge periodicity of checkerboard textures is locked to 4 unit cells over a wide doping range. In addition we find that checkerboard structures are favored at surfaces.