A Superconducting Instability in the Infinite-U Anderson Lattice in the Presence of Crystal Electric Fields

TL;DR

This paper demonstrates a superconducting instability with T1g symmetry in the infinite-U Anderson lattice influenced by cubic crystal fields, using slave boson techniques and advanced Green function calculations.

Contribution

It introduces a novel analysis of superconductivity in the Anderson lattice considering crystal electric fields and employs the analytic tetrahedron method for Green function calculations.

Findings

Superconducting instability with T1g symmetry identified.

No pairing in the A1g s-wave channel due to repulsion.

Weakly repulsive interactions in T2g channel.

Abstract

We report evidence of a superconducting instability (of $T_{1g}$ symmetry) in the infinite-U Anderson lattice in the presence of crystal fields of cubic symmetry. We assume a lattice of $4f$ sites, each with a total angular momentum of $J=5/2$ that is split by crystal fields into a low-lying doublet of $\Gamma_7$ symmetry and an excited quartet of $\Gamma_8$ symmetry. Slave Bosons on the $4f$ sites create and destroy $4f^0$ configurations and Lagrange multipliers at each $4f$ site enforce the occupancy constraint due to the infinite Coulomb repulsion. Quasiparticle interactions are due to exchange of $4f$ density fluctuations, which are represented by fluctuations in the slave Bosons and Lagrange multipliers. We use the so-called analytic tetrahedron method to calculate the dressed (to order 1/N) Boson Green functions. In weak couping, the exchange of the dressed Bosons gives rise to a superconducting instability of $T_{1g}$, $xy(x^2-y^2)$, symmetry. The $A_{1g}$, ``s-wave'', channel has strongly repulsive interactions and hence no pairing instability. The $T_{2g}$ channel exhibits weakly repulsive interactions. Average quasiparticle interactions in the $E_g$, $x^2-y^2$, $3z^2-r^2$, channel fluctuate strongly as a function of the number of tetrahedra used to calculate the Bosonic Green functions,