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We report the discovery of two-phase unconventional superconductivity inCeRh$_2$As$_2$. Using thermodynamic probes, we establish that thesuperconducting critical field of its high-field phase is as high as 14 T,remarkable in a material whose transition temperature is 0.26 K. Furthermore, a$c$-axis field drives a transition between two different superconductingphases. In spite of the fact that CeRh$_2$As$_2$ is globally centrosymmetric,we show that local inversion-symmetry breaking at the Ce sites enables Rashbaspin-orbit coupling to play a key role in the underlying physics. More detailedanalysis identifies the transition from the low- to high-field states to beassociated with one between states of even and odd parity.

Field-induced transition from even to odd parity superconductivity in CeRh$_2$As$_2$