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

TL;DR

This study develops a symmetry-informed framework combining Bogoliubov–de Gennes and Landau theories to unravel the complex order-parameter structure in CeRh$_2$As$_2$, a layered, locally noncentrosymmetric heavy-fermion superconductor. It identifies a dominant low-field even-parity $B_{1g+}$ pairing and a competing high-field odd-parity $B_{1u+}/B_{2u+}$ sector, whose near-degeneracy is governed by the hierarchy of normal-state energy scales set by intralayer SOC and interlayer hopping. A key result is a symmetry-preserving first-order transition between coexistence phases of the same overall symmetry, driven by trilinear couplings to an antiferromagnetic order parameter $A_{1u-}$, with a possible critical endpoint and crossover region. The framework reproduces experimental phase diagrams for varying temperature, field direction, and field strength, and makes testable predictions for thermodynamic signatures, Knight shifts, and the coexistence of multicomponent superconductivity with magnetism in CeRh$_2$As$_2$.

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.

Figures (13)

• Figure 1: Schematic of the $\mathrm{CeRh_2As_2}$ level splitting with the inset showing the crystal structure with distinct lattice planes. The f-orbital degeneracy is lifted by strong spin-orbit coupling and the $J = 5/2$ multiplet of Ce$^{3+}$ is split by the crystal electric field into three Kramers doublets khim_field-induced_2021hafner_possible_2022.
• Figure 2: The three linearly independent translationally invariant magnetic orders consistent with the absence of a magnetic field at the $\mathrm{As}(1)$ sites. All linear combination are also compatible with the NQR experiments kibune_observation_2022. Configurations (b) and (c) are degenerate.
• Figure 3: Irreducible representations of possible magnetic orders for (a)--(d) the $\mathrm{As}(1)$ and (e)--(h) the $\mathrm{As}(2)$ sites: (a), (e) out-of-plane FM, (b), (f) out-of-plane AFM, (c), (g) in-plane FM, and (d), (h) in-plane AFM. The corresponding irreps are given in all panels.
• Figure 4: Proposed out-of-plane AFM $A_{1u-}$ order of $\mathrm{CeRh_2As_2}$ with zero field at $\mathrm{As}(1)$ and nonzero field at $\mathrm{As}(2)$ sites.
• Figure 5: Phase diagram for out-of-plane magnetic field and $T_N > T_c$ for (a) the full temperature and magnetic-field range and (b) the region close to the end point of the first-order transition. The colors of distinct phases are generated by mixing contributions from the even-parity OP $|\Delta_1|$ (blue), the odd-parity OP $|\Delta_2|$ (red), and the magnetic OP $|M|$ (green) into an RGB-triplet. The transparency is determined from the overall OP magnitude. Solid and dotted lines represent first-order and second-order phase transitions, respectively.