Superconductivity and Antiferromagnetism in Three-Dimensional Hubbard model

TL;DR

This paper investigates the interplay between antiferromagnetism and superconductivity in a 3D Hubbard model, revealing phase diagram evolutions, coexistence phases, and resonance phenomena using spin fluctuation theory.

Contribution

It introduces a detailed analysis of phase transitions and coexistence of antiferromagnetism and superconductivity in a 3D Hubbard model with anisotropic transfer, extending previous 2D studies.

Findings

Antiferromagnetic phase expands with increasing anisotropy ratio.

Superconducting phase shrinks as antiferromagnetic order dominates.

Resonance peaks persist in 3D d-wave superconducting phase.

Abstract

Interplay between antiferromagnetism and superconductivity is studied by using the 3-dimensional nearly half-filled Hubbard model with anisotropic transfer matrices $t_{\rm z}$ and $t_{\perp}$. The phase diagrams are calculated for varying values of the ratio $r_{\rm z}=t_{\rm z}/t_{\perp}$ using the spin fluctuation theory within the fluctuation-exchange approximation. The antiferromagnetic phase around the half-filled electron density expands while the neighboring phase of the anisotropic $d_{x^{2}-y^{2}}$-wave superconductivity shrinks with increasing $r_{\rm z}$. For small $r_{\rm z}$ $T_{\rm c}$ decreases slowly with increasing $r_{\rm z}$. For moderate values of $r_{\rm z}$ we find the second order transition, with lowering temperature, from the $d_{x^{2}-y^{2}}$-wave superconducting phase to a phase where incommensurate SDW coexists with $d_{x^{2}-y^{2}}$-wave superconductivity. Resonance peaks as were discussed previously for 2D superconductors are shown to survive in the $d_{x^{2}-y^{2}}$-wave superconducting phase of 3D systems. Soft components of the incommensurate SDW spin fluctuation mode grow as the coexistent phase is approached.