$H-T$ Phase diagram of CeRh$_{2}$As$_{2}$: Refinement of the parity-switch scenario

Abstract

The superconductivity of CeRh$_2$As$_2$ has drawn attention due to its first-order transition in magnetic fields. At first glance, the multiple superconducting (SC) phases as well as the first-order transition appear consistent with the parity-switch scenario, which emphasizes the role of strong Rashba spin-orbit coupling enabled by the locally non-centrosymmetric crystal structure. However, experimental phase diagrams exhibit notable deviations from this simple picture: thermodynamic measurements reveal a nearly vertical phase boundary of the high-field SC phase despite the orbital depairing effect, while transport measurements show that the initial slope of the high-field SC phase is steeper than that of the low-field SC phase. Here, we show that these discrepancies can be understood by considering the combined effects of nonsymmorphic band structure and coexisting antiferromagnetic order. We demonstrate that the symmetry-enforced electronic structure around the Dirac node and type-II Van Hove saddle points near the X point in the Brillouin zone boundary becomes more anisotropic with increased interlayer hopping amplitude, and this anisotropic band structure naturally accounts for the anomalous initial slope of the odd-parity SC phase. Meanwhile, a phenomenological theory incorporating coexisting antiferromagnetism explains the nearly vertical thermodynamic phase boundary as a consequence of field-enhanced odd-parity superconductivity enabled by the over-suppression of Pauli depairing.