Intrinsic Berry phase contribution to Hall conductivity in CoS$_2$

In Weyl semi-metals, the conduction and valence bands intersect at distinct points on the Brillouin zone (Weyl points), which act as monopoles of Berry curvature in momentum space. This nontrivial band topology, identified from electronic structure calculations, gives rise to various exotic magneto-transport properties. Hybrid functional calculations that incorporate a portion of exact exchange, magneto-transport measurements, and temperature-dependent resistivity confirm nontrivial band topology and half-metallicity in CoS$_2$ of magnetic ordering temperature $T_{\rm C} \approx 120~\mathrm{K}$. However, electronic structure calculations also show that application of small strain transforms this half metallic character to the metallic. Interestingly, the magnetoresistance (MR) of the CoS$_2$ films is characterized by a reentrant weak localization above a critical field at $T \leq 60\,\mathrm{K}$ and a negative to positive transition in MR as the $T$ goes from $<T_{\rm C}$ to $>T_{\rm C}$. Experimental observation of anomalous Hall resistivity and $ab~initio$ computed band structure, Berry curvature, and Hall conductivity ($\sigma_{xy}$) demonstrate that the $\sigma_{xy}$ in CoS$_2$ is primarily driven by the intrinsic Karplus-Luttinger contribution, often linked to Berry phase physics.