Superconductivity with peculiar upper critical fields in quasi-one-dimensional Cr-based pnictides

The discovery of superconductivity in quasi-one-dimensional Cr-based pnictides A ₂Cr₃As₃ (A = alkali metals) has generated considerable research interest, primarily owing to their reduced dimensionality, significant electron correlations, and possible unconventional superconductivity. The upper critical field ($H_{c2}$) provides important information on the superconducting pairing. In this paper, we first briefly overview the latest research progress on the Cr-based superconductors. Then, we introduce typical $H_{c2}\left(T\right)$ behaviors of type-II superconductors in relation with the pair-breaking mechanisms. After a description of the measurement method for $H_{c2}$, we focus on the analysis of $H_{c2}$ data, especially for the temperature and angle dependence, in K₂Cr₃As₃ crystals. The result indicates (i) an absence of Pauli-paramagnetic pair breaking for field perpendicular to the Cr₃As₃ chains, and (ii) a unique threefold modulation for the in-plane $H_{c2}\left(\varphi \right)$ profile. Finally we conclude with remarks on the possible unconventional superconducting pairing symmetry. (topical review)