We report two distinct superconducting states with different crystal structures and a crossover from a type-II to a type-I superconductor (SC) in $(\mathrm{Ba},\mathrm{Sr})\mathrm{B}{\mathrm{i}}_3$. The superconducting parameters are revealed to classify two SCs: $\mathrm{BaB}{\mathrm{i}}_3$ is in the weak-coupling limit on the basis of $\mathrm{\Delta }C/{\gamma }_{\mathrm{n}}{T}_{\mathrm{c}}\sim 0.67$ and $2\mathrm{\Delta }/k_{\mathrm{B}}{T}_{\mathrm{c}}\sim 3.28$ while $\mathrm{SrB}{\mathrm{i}}_3$ is a strong-coupling SC with $\mathrm{\Delta }C/{\gamma }_{\mathrm{n}}{T}_{\mathrm{c}}\sim 2.41$ and $2\mathrm{\Delta }/k_{\mathrm{B}}{T}_{\mathrm{c}}\sim 6.09$. A large Kadowaki-Woods ratio $(R_{\mathrm{KW}}\sim 3.53a_0)$ suggests an enhanced electron-electron scattering in $\mathrm{BaB}{\mathrm{i}}_3$. With increasing the pressure, the $T_{\mathrm{c}}$ of $\mathrm{BaB}{\mathrm{i}}_3$ decreases linearly at first, and then shows an abrupt increase up to 6.2 K at 0.88 GPa. This behavior can be attributed to a pressured-induced structural transition and the resulting variations of spin-orbit coupling and Fermi structures. $T_{\mathrm{c}}$ of $\mathrm{SrB}{\mathrm{i}}_3$ is suppressed monotonously by pressure. The Ginzburg-Landau parameter ${\kappa }_{\mathrm{GL}}$ of $\mathrm{BaB}{\mathrm{i}}_3$ decreases from 10.35 at ambient pressure (AP) to 0.86 at 1.75 GPa, and then tends to saturation. ${\kappa }_{\mathrm{GL}}$ of $\mathrm{SrB}{\mathrm{i}}_3$ decreases from 0.76 at AP to $1/\phantom{1\sqrt{2}}\sqrt{2}$ at 1.20 GPa, which manifests pressured-induced crossover from a type-II to a type-I SC. Possible physical mechanisms are proposed.

• Received 18 July 2018
• Revised 19 September 2018

DOI:https://doi.org/10.1103/PhysRevB.98.220506