We present a comprehensive study of the critical current densities and the superconducting vortex phase diagram in the stoichiometric superconductor ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ which has a critical temperature of $\sim 35\mathrm{K}$. We performed detailed magnetization measurements both of high quality single crystals for different orientations in an applied magnetic field up to 16 T and for a powder sample. We find an extremely large critical current density, $J_c$, up to ${10}^8\mathrm{A}/{\mathrm{cm}}^2$ for single crystals when $H\parallel \left(ab\right)$ at $5\mathrm{K}$, which remains robust in fields up to $16\mathrm{T}$, being the largest of any other iron-based superconductor. The critical current density is reduced by a factor 10 in single crystals when $H\parallel c$ at 5 K and significantly suppressed by the presence of grain boundaries in the powder sample. We also observe the presence of the fishtail effect in the magnetic hysteresis loops of single crystals when $H\parallel c$. The flux pinning force density and the pinning parameters suggest that the large critical current could be linked to the existence of point core and surface pinning. Based on the vortex phase diagram and the large critical current densities, ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ is now established as a potential iron-based superconductor candidate for practical applications.

Understanding superconductivity requires detailed knowledge of the normal electronic state from which it emerges. A nematic electronic state that breaks the rotational symmetry of the lattice can potentially promote unique scattering relevant for superconductivity. Here, we investigate the normal transport of superconducting ${\mathrm{FeSe}}_{1-x}{\mathrm{S}}_x$ across a nematic phase transition using high-magnetic fields up to 69 T to establish the temperature and field dependencies. We find that the nematic state is dominated by a linear resistivity at low temperatures that evolves towards Fermi-liquid behavior, depending on the composition $x$ and the impurity level. Near the nematic end point, we find an extended temperature regime with $\sim T^{1.5}$ resistivity, different from the behavior found near an antiferromagnetic critical point. The variation of the resistivity exponent with temperature reflects the importance of the nematoelastic coupling that can also suppress divergent critical fluctuations at the nematic end point. The transverse magnetoresistance inside the nematic phase has a $\sim H^{1.55}$ dependence over a large magnetic field range and it displays an unusual peak at low temperatures inside the nematic phase. Our study reveals anomalous transport inside the nematic phase, influenced by both changes in the electronic structure and the scattering with the lattice and spin fluctuations.

The discovery of iron-based superconductors (FBS) and their superconducting properties has generated huge research interest and provided a very rich physics high T_c family for fundamental and experimental studies. The 1111 (REFeAsO, RE = Rare earth) and 1144 (AEAFe₄As₄, AE = Ca, Eu; A = K, Rb) families are the two most important families of FBS, which offer the high T_c of 58 K and 36 K with doping and without doping, respectively. Furthermore, the crystal growth of these families is not an easy process, and a lot of efforts have been reported in this direction. However, the preparation of high-quality and suitable-sized samples is still challenging. In this short review, we will summarize the growth of materials with their superconducting properties, especially polycrystals and single crystals, for the 1111 and 1144 families, and make a short comparison between them to understand the developmental issues.

CaKFe ₄ As ₄ (1144) is a unique stoichiometric iron-based superconductor which harbors high upper critical fields and large critical current densities. In this work, we describe a study to optimize the synthesis conditions of stoichiometric polycrystalline samples of CaKFe ₄ As ₄ and assess their structural, magnetic and transport properties. The samples were prepared over a wide temperature range (900 °C–1100 °C) and the pure phase formation is centered around 955 °C. Outside this temperature region, impurity phases of KFe ₂ As ₂ and CaFe ₂ As ₂ can also form. Magnetic susceptibility and resistivity measurements establish that the critical temperature reaches ∼34 K for the optimum synthesis conditions and the critical current reaches 2 × 10 ⁴ A cm ⁻² . The post-annealing process demonstrates the stability of the 1144 phase up to 500 °C, however, under higher temperature annealing, phase degradation occurs. Our study indicates that the formation of phase-pure 1144 occurs over a much narrower window and its highly prone to multi-phase formation as compared with the 122 family. As a result, the superconducting properties are enhanced for the pure 1144 phase but they are likely to be affected by the inter- and intra-granular behavior originating from the microstructural nature of polycrystalline CaKFe ₄ As ₄ , similar to other iron-based superconductors. Based on our study, we construct the phase diagram for polycrystalline 1144 and compared it with that reported for 1144 single crystal.