Evolution of superconductivity from charge clusters to stripes in the $t$-$t'$-$J$ model

TL;DR

This study uses tensor network simulations to explore how charge fluctuations and hole clustering influence the development of superconductivity in the $t$-$t'$-$J$ model, revealing a transition from localized to coherent pairing.

Contribution

It provides a detailed microscopic picture of how charge clustering and stripe formation relate to superconductivity in cuprates, connecting theory with experimental observations.

Findings

Pairing correlations are localized on hole clusters at intermediate temperatures.

Delocalization of pairing occurs as stripe order develops at lower temperatures.

The results align with STM and NMR experimental evidence in cuprates.

Abstract

Competition and coexistence of charge orders and superconductivity are hallmarks in many strongly correlated electron systems. Here, we unravel the precise role of charge fluctuations on the superconducting state in the $t$-$t'$-$J$ model of the high-temperature cuprate superconductors. Using finite-temperature tensor network simulations, we investigate thermal snapshots in the underdoped regime where the ground state features a superconducting stripe phase. At intermediate temperatures, where stripes have melted and hole clustering is observed, we find that pairing correlations are tightly localized on the hole clusters. Upon entering the stripe regime at lower temperatures, pairing increasingly delocalizes across different hole clusters to ultimately become coherent across the full system in the ground state. This pair-charge locking gives rise to an intuitive picture of the parent state of the superconducting stripe phase: pairing is localized on hole clusters formed via hole attraction due to the onset of magnetic correlations at intermediate temperature. We discuss how this microscopic picture is consistent with a broad range of experimental observations in cuprate superconductors, including scanning tunneling microscopy (STM) evidence for local pairing above $T_c$ and nuclear magnetic resonance (NMR) signatures of charge clustering in the underdoped regime.