# Period 4 stripe in the extended two-dimensional Hubbard model

## TL;DR

This study uses advanced tensor network methods to analyze stripe and superconducting states in the extended 2D Hubbard model, revealing how next-nearest neighbor hopping influences stripe periods and their coexistence with superconductivity, aligning with experimental observations.

## Contribution

It provides the first detailed tensor network analysis of stripe periods and superconductivity in the extended Hubbard model at 1/8 doping, highlighting the role of next-nearest neighbor hopping.

## Key findings

- Stripe period decreases with increasing negative $t'$.
- Period 4 stripes match experimental data for cuprates.
- Superconductivity coexists with period 4 stripes at higher doping levels.

## Abstract

We study the competition between stripe states with different periods and a uniform $d$-wave superconducting state in the extended 2D Hubbard model at 1/8 hole doping using infinite projected entangled-pair states (iPEPS). With increasing strength of negative next-nearest neighbor hopping $t'$, the preferred period of the stripe decreases. For the values of $t'$ predicted for cuprate high-T$_c$ superconductors, we find stripes with a period 4 in the charge order, in agreement with experiments. Superconductivity in the period 4 stripe is suppressed at $1/8$ doping. Only at larger doping, $0.18 \lesssim \delta < 0.25$, the period 4 stripe exhibits coexisting $d$-wave superconducting order. The uniform $d$-wave state is only favored for sufficiently large positive $t'$.