Anisotropic superconductivity in ZrB$_{12}$ near critical Bogomolnyi point

TL;DR

This study demonstrates that ZrB$_{12}$ exhibits anisotropic superconductivity with field-direction dependent type-I and type-II behaviors, serving as a model system to explore inter-type superconductivity near the critical Bogomolnyi point.

Contribution

The paper provides experimental evidence of anisotropic superconductivity in ZrB$_{12}$ near the critical B-point, aligning with theoretical predictions for such systems.

Findings

ZrB$_{12}$ shows anisotropic superconducting properties.

Superconducting behavior varies with magnetic field direction.

ZrB$_{12}$ is a suitable model for inter-type anisotropic superconductivity.

Abstract

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