Exposing the odd-parity superconductivity in CeRh$_2$As$_2$ with hydrostatic pressure

Odd-parity superconductivity is a fundamentally interesting but rare state of matter with a potential for applications in topological quantum computing. Crystals with staggered locally noncentrosymmetric structures have been proposed as platforms where a magnetic field can induce a transition between even- and odd-parity superconducting (SC) states. The strongly correlated superconductor CeRh$_2$As$_2$ with the critical temperature $T_{\mathrm{c}}\approx0.4\,\mathrm{K}$ is likely the first example material showing such a phase transition, which occurs at the magnetic field $\mu_{0}H^{*}=4\,\mathrm{T}$ applied along the crystallographic $c$ axis. CeRh$_2$As$_2$ also undergoes a phase transition of an unknown origin at $T_{0}=0.5\,\mathrm{K}$. By subjecting CeRh$_2$As$_2$ to hydrostatic pressure and mapping the resultant changes to the SC phase diagrams we investigated how the lattice compression and changes to the electronic correlations affect the stability and relative balance of the two SC states. The abnormally high in-plane upper critical field becomes even higher close to a quantum critical point of the $T_{0}$ order. Remarkably, the SC phase-switching field $H^{*}$ is drastically reduced under pressure, dropping to $0.3\,\mathrm{T}$ at $2.7\,\mathrm{GPa}$. This result signals an apparent strengthening of the local noncentrosymmetricity and forecasts a possible stabilization of the putative odd-parity state down to zero field, hitherto not considered by theoretical models.