标题： CeRh$_{2}$As$_{2}$的磁场相图（外加磁场） 显示英文标题

标题： The phase diagram of CeRh$_{2}$As$_{2}$ for out-of-plane magnetic field

摘要： 重费米子超导体CeRh$_{2}$As$_{2}$ ($T_{\textrm{c}} = 0.35\, \textrm{K}$) 在磁场平行于四方晶胞的$c$轴时显示出两种超导相（SC1和SC2）。迄今为止的所有实验表明，在$\mu_{\textrm{0}}H^{*} \approx 4\, \textrm{T}$检测到的超导序参量的变化是由于Ce位点处由局域非中心对称环境引起的强Rashba自旋-轨道耦合，而这种结晶结构在整体上是中心对称的。该材料在低于$T_{\textrm{0}} = 0.54\, \textrm{K}$的温度下还存在另一种相（相I）。在之前的一项比热研究中[K. Semeniuk等，Phys. Rev. B, $107$, L220504 (2023)] 我们已经证明相I可以持续到一个大于 $H^{*}$ 的场强 $\mu_{\textrm{0}}H_{0} \approx 6\, \textrm{T}$。 基于热力学的论证，我们预期相-I边界线会在四重临界点处穿过相SC2。 然而，我们在相SC2内部无法找到相-I线的任何迹象，并推测这是由于 $T_{0}(H)$ 线几乎垂直于 $H$ 轴，因此对依赖于 $T$ 的测量来说是不可见的。 这表明两种有序参数之间存在微弱的竞争。 在这里，我们报道了高质量单晶材料在磁场依赖下的磁致伸缩和交流磁化率测量结果。 我们在相SC2内部清楚地观察到了 $H_{0}$ 处的奇异性，并证实了我们的先前预测。 此外，我们在依赖于$T$的比热测量中观察到跨越$T^{*}(H)$线的转变，结果显示$T^{*}(H)$线并非与场轴垂直，而是具有正斜率。 我们的工作支持最近的$\mu$SR 结果，该结果表明相 I 与超导性的共存。 显示英文摘要

摘要： The heavy-fermion superconductor CeRh$_{2}$As$_{2}$ ($T_{\textrm{c}} = 0.35\, \textrm{K}$) shows two superconducting (SC) phases, SC1 and SC2, when a magnetic field is applied parallel to the $c$ axis of the tetragonal unit cell. All experiments to date indicate that the change in SC order parameter detected at $\mu_{\textrm{0}}H^{*} \approx 4\, \textrm{T}$ is due to strong Rashba spin-orbit coupling at the Ce sites caused by the locally non-centrosymmetric environments of the otherwise globally centrosymmetric crystalline structure. Another phase (phase I) exists in this material below $T_{\textrm{0}} = 0.54\, \textrm{K}$. In a previous specific heat study [K. Semeniuk et al. Phys. Rev. B, $107$, L220504 (2023)] we have shown that phase I persists up to a field $\mu_{\textrm{0}}H_{0} \approx 6\, \textrm{T}$, larger than $H^{*}$. From thermodynamic arguments we expected the phase-I boundary line to cross phase SC2 at a tetracritical point. However, we could not find any signature of the phase-I line inside the SC2 phase and speculated that this was due to the fact that the $T_{0}(H)$ line is almost perpendicular to the $H$ axis and, therefore, invisible to $T$-dependent measurements. This would imply a weak competition between the two order parameters. Here, we report magnetic field dependent measurements of the magnetostriction and ac-susceptibility on high-quality single crystals. We see clear evidence of the singularity at $H_{0}$ inside the SC2 phase and confirm our previous prediction. Furthermore, we observe the transition across the $T^{*}(H)$ line in $T$-dependent specific heat measurements, which show that the $T^{*}(H)$ line is not perpendicular to the field axis, but has a positive slope. Our work supports recent $\mu$SR results which suggest coexistence of phase I with superconductivity.