Perturbation Analysis of Superconductivity in the Trellis-Lattice Hubbard Model

TL;DR

This study analyzes superconductivity in the trellis-lattice Hubbard model, revealing stable spin-singlet states and potential spin-triplet pairing under certain conditions, with implications for materials like Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}.

Contribution

It applies third-order perturbation theory to investigate pairing symmetry and transition temperatures in the trellis-lattice Hubbard model, highlighting conditions for different superconducting states.

Findings

Spin-singlet state is very stable across many parameters.

Spin-triplet superconductivity may occur away from half-filling with small band gaps.

Discussion of unconventional pairing in Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$.

Abstract

We investigate pairing symmetry and transition temperature in the trellis-lattice Hubbard model. We solve the \'Eliashberg equation using the third-order perturbation theory with respect to the on-site repulsion $U$. We find that a spin-singlet state is very stable in a wide range of parameters. On the other hand, when the electron number density is shifted from the half-filled state and the band gap between two bands is small, a spin-triplet superconductivity is expected. Finally, we discuss a possibility of unconventional superconductivity and pairing symmetry in Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$.