Electronic States and Superconducting Transition Temperature based on the Tomonaga-Luttinger liquid in Pr$_{2}$Ba$_{4}$Cu$_{7}$O$_{15-\delta}$

TL;DR

This paper investigates the electronic structure and superconducting transition temperature of Pr$_{2}$Ba$_{4}$Cu$_{7}$O$_{15- ext{delta}}$ using GGA calculations and Tomonaga-Luttinger liquid theory, proposing a 1D superconductivity mechanism in CuO double chains.

Contribution

It combines first-principles calculations with Luttinger liquid theory to explain the superconductivity in Pr247 as a quasi-1D phenomenon, providing a theoretical estimate of $T_c$ consistent with experiments.

Findings

Fermi surface of CuO double chains is quasi-1D.

Estimated $T_c$ aligns with experimental values.

Superconductivity mechanism explained via Tomonaga-Luttinger liquid theory.

Abstract

An NQR experiment revealed superconductivity of Pr$_2$Ba$_4$Cu$_7$O$_{15-\delta}$ (Pr247) to be realized on CuO double chain layers and suggests possibility of novel one-dimensional(1D) superconductivity. To clarify the nature of the 1D superconductivity, we calculate the band dispersions of Pr247 by using the generalized gradient approximation(GGA). It indicates that Fermi surface of CuO double chains is well described to the electronic structure of a quasi-1D system. Assuming the zigzag Hubbard chain model to be an effective model of the system, we derive tight binding parameters of the model from a fit to the result of GGA. Based on the Tomonaga-Luttinger liquid theory, we estimate transition temperature ($T_c$) of the quasi-1D zigzag Hubbard model from the calculated value of the Luttinger liquid parameter $K_{\rho}$. The result of $T_c$ is consistent with that of experiments in Pr247 and it suggests that the mechanism of the superconductivity is well understood within the concept of the Tomonaga-Luttinger liquid.