Spin-fluctuation-mediated chiral $d+id'$-wave superconductivity in the $\alpha$-$\mathcal{T}_3$ lattice with an incipient flat band

TL;DR

This paper investigates chiral $d+id'$-wave superconductivity in the $ ext{α-} ext{T}_3$ lattice, revealing a spin-fluctuation mechanism mediated by incipient flat bands that leads to topologically nontrivial pairing states.

Contribution

It demonstrates the emergence of chiral $d+id'$-wave superconductivity with high Chern numbers driven by spin fluctuations in a nearly quarter-filled $ ext{α-} ext{T}_3$ lattice.

Findings

Identifies two chiral $d+id'$-wave phases with different Chern numbers.

Shows spin fluctuations from an incipient flat band mediate pairing.

Finds a $d+id'$-wave state with Chern number 8 from the Eliashberg equation.

Abstract

We study anisotropic superconductivity in the nearly quarter-filled $\alpha$-$\mathcal{T}_3$ lattice. We analyze an extended Hubbard model with off-site attractive interactions within the mean-field framework and find two distinct chiral $d+id'$-wave superconducting phases characterized by different Chern numbers. We further investigate the superconducting mechanism mediated by spin fluctuations arising from purely repulsive interactions by applying the fluctuation-exchange (FLEX) approximation to the Hubbard model. The gap symmetry obtained by solving the linearized Eliashberg equation is $d$-wave, which corresponds to a $d+id'$-wave superconducting state with a Chern number of $8$, including the spin degree of freedom. The $\mathbf{q}=\mathbf{0}$ antiferromagnetic spin fluctuation, which possesses the largest spectral weight at finite energies arising from the incipient flat band, gives rise to an effective spin-singlet pairing glue between rim sites.