Anisotropic superconductivity in ZrB12 near the critical Bogomolnyi point

The superconductors with the Ginzburg-Landau (G-L) parameter ($\\kappa$)\n$\\sim1/\\sqrt{2}$ exist near a critical Bogolomonyi (B) point where they show\ninter-type domains between type-I and type-II superconductivity. While such\nphysics is well understood for isotropic superconductors, the experimental\ninvestigation of the physics of anisotropic superconductors near a critical\nB-point remains an unattained goal mainly due to the unavailability of model\nmaterial systems. Theoretically, such superconductors are expected to show\ntype-I or type-II behaviour for definite directions of an applied magnetic\nfield. Here, from directional point-contact Andreev reflection spectroscopy and\nfield-angle dependent ac magnetic susceptibility measurements, we show that\nZrB$_{12}$ is an anisotropic superconductor, and it exhibits field-direction\ndependent type-I and type-II behaviour. These observations match remarkably\nwell with the theoretical expectations for an anisotropic superconductor near a\ncritical B-point. Therefore, our results project ZrB$_{12}$ as a model material\nsystem where the physics of inter-type anisotropic superconductivity can be\nexplored experimentally.\n