Superconductivity and Spin gap in the zigzag chain t-J model simulating a CuO double chain in Pr_2Ba_4Cu_7O_15-delta

TL;DR

This study uses numerical methods to analyze a zigzag chain t-J model representing a CuO double chain, revealing conditions for superconductivity and a significant spin gap consistent with experimental observations.

Contribution

It provides a detailed phase diagram of the spin gap and superconductivity in the model, connecting theoretical predictions with experimental data for Pr_2Ba_4Cu_7O_15- extdelta.

Findings

Superconductivity occurs in parameter regions matching experiments.

A large spin gap, up to 100K, is predicted in realistic conditions.

Phase boundary at half-filling aligns with known frustrated quantum spin systems.

Abstract

Using the numerical diagonalization method, we examine the one-dimensional t_1-t_2-J_1-J_2 model (zigzag chain t-J model) which represents an effective model for metallic CuO double chain in the superconductor Pr_2Ba_4Cu_7O_15-\delta. Based on the Tomonaga-Luttinger liquid theory, we calculate the Luttinger-liquid parameter K_\rho as a function of electron density n. It is found that superconductivity is realized in parameter region corresponding to the experimental result. We show phase diagram of spin gap on the t_2/|t_1|-n plane by analyzing the expectation value of twist-operator Z_\sigma in the spin sector. The spin gap appears in the region with large t_2/|t_1|, where the phase boundary at half-filling is consistent with that of the known frustrated quantum spin system. The analysis also suggests that the estimated value of the spin gap reaches 100K in the realistic parameter region of Pr_2Ba_4Cu_7O_15-delta.