Composite Superconducting Orders and Magnetism in CeRh$_2$As$_2$

TL;DR

This paper develops a theoretical framework to understand the complex interplay of superconductivity and magnetism in CeRh$_2$As$_2$, explaining experimental phase diagrams and proposing symmetries of the superconducting states.

Contribution

It introduces a symmetry-based theoretical approach combining Bogoliubov--de Gennes and Landau methods to analyze superconducting and magnetic phases in CeRh$_2$As$_2$, revealing the role of spin-orbit coupling.

Findings

Reproduces experimental phase diagrams under various magnetic fields and temperatures.

Explains near degeneracy of pairing symmetries via intralayer spin-orbit coupling.

Interprets first-order transition as coexistence phase transition with potential critical endpoint.

Abstract

Locally noncentrosymmetric materials are attracting significant attention due to the unique phenomena associated with sublattice degrees of freedom. The recently discovered heavy-fermion superconductor CeRh$_2$As$_2$ has emerged as a compelling example of this class, garnering widespread interest for its remarkable temperature-magnetic-field phase diagram, which features a field-induced first-order superconductor-to-superconductor phase transition with nontrivial dependence on the field direction and high critical fields, as well as antiferromagnetic and potentially higher multipole orders. To investigate the complex interplay of the ordered phases in CeRh$_2$As$_2$, we develop a theoretical framework based on symmetry analysis combined with Bogoliubov--de Gennes and Landau methods. This approach allows us to propose probable symmetries of the superconducting states and elucidate their close relationship with magnetism. Among other results, we find that the near degeneracy of two pairing symmetries is naturally explained if and only if intralayer spin-orbit coupling is large compared to interlayer hopping. Intriguingly, we find that the first-order transition can be interpreted as a transition between coexistence phases of the same superconducting order parameters, albeit with distinct admixtures. This line may end in a critical endpoint below the superconducting critical temperature. Our approach accurately reproduces current experimental phase diagrams for varying temperature as well as out-of-plane and in-plane magnetic field, both if the transition to a magnetic phase occurs below the superconducting critical temperature and if it occurs above. Furthermore, we calculate the magnetic susceptibility and the specific heat and compare these quantities to recent experimental results.