Kondo Lattice model for field induced triplet pairing in CeRh$_2$As$_2$

Spin triplet superconductors are of interest because of their topological properties, and their robustness to high magnetic fields. CeRh$_2$As$_2$ is a unique heavy fermion superconductor with both even-parity and candidate odd-parity superconducting phases with a special feature enabling a field induced phase transition between the two. The field induced transition which switches the parity of the Cooper pairs is enabled by a staggered antisymmetric spin orbit coupling (ASOC) interaction. However, the heavy fermion origins of the superconductivity in CeRh$_2$As$_2$ and the origin of the antisymmetric spin-orbit coupling are currently unexplored. Here, we develop a Kondo lattice model for CeRh$_2$As$_2$ and demonstrate how local hybridization between Cerium $d$- and $f$-orbitals, driven by the locally broken inversion symmetry, at the Cerium sites generates the ASOC. The resulting Kondo lattice model leads to nearly degenerate even and odd parity superconducting states that display a field induced parity transition between an even-parity state and an odd-parity pseudospin triplet state. We discuss the wider implications of our results extended to other heavy fermion systems like CeSiI.