Superconductivity arising from layer-differentiation in multi-layer cuprates

TL;DR

This study uses a three-layer Hubbard model and TPSC approach to reveal how layer differentiation influences superconductivity and antiferromagnetism in multi-layer cuprates, highlighting the role of electron correlations and inter-layer processes.

Contribution

It demonstrates that outer CuO$_2$ planes dominate superconductivity while inner planes dominate antiferromagnetism, and shows inter-layer pair scattering enhances $T_c$ in multi-layer cuprates.

Findings

OPs dominate $d_{x^{2}-y^{2}}$-wave superconductivity

IP dominates antiferromagnetism due to stronger correlations

Inter-layer pair scattering increases $T_c$ in trilayer systems

Abstract

In order to theoretically identify the factors governing superconductivity in multi-layer cuprates, a three-layer Hubbard model is studied with the two-particle self-consistent (TPSC) approach so as to incorporate electron correlations. The linearized Eliashberg equation is then solved for the gap function in a matrix form to resolve the role of outer CuO$_2$ planes (OPs) and inner plane (IP). We show that OPs dominate IP in the $d_{x^{2}-y^{2}}$-wave superconductivity, while IP dominates in the antiferromagnetism. This comes from an electron correlation effect in that the correlation makes the doping rates different between OPs and IP (i.e., a self-doping effect), which occurs in intermediate and strong correlation regimes. Namely, the antiferromagnetic fluctuations in IP are stronger due to a stronger electron correlation, which simultaneously reduces the quasiparticle density of states in IP with a suppressed $d_{x^{2}-y^{2}}$-wave superconductivity. Intriguingly, while the off-diagonal (inter-layer) elements in the gap function matrix are tiny, {\it inter-layer pair scattering} processes are in fact at work in enhancing the superconducting transition temperature $T_{\text{c}}$ through the inter-layer Green's functions. This actually causes the trilayer system to have higher $T_{\text{c}}$ than the single-layer in a weak- and intermediate-coupling regimes. This picture holds for a range of the on-site Hubbard repulsion $U$ that contains those estimated for the cuprates. The present result is qualitatively consistent with nuclear magnetic resonance experiments in multi-layer cuprates superconductors.