Microscopic origin of the competition between charge density waves and enhanced superconductivity in Ba(Ni,Co)$_2$(As,P)$_2$

Nematic phase transitions in high-temperature superconductors have a strong impact on the electronic properties of these systems. BaFe$_2$As$_2$,@ with an established nematic transition around 137 K induced by magnetic fluctuations, and BaNi$_2$As$_2$,@ a non-magnetic analog of BaFe$_2$As$_2$ with a structural transition in the same temperature range,@ share a common tetragonal aristotype crystal structure with space-group type $I4/mmm$.@ In contrast to BaFe$_2$As$_2$ where collinear stripe magnetic order is found for the low-$T$ phase, a unidirectional charge density wave is observed for the low-$T$ phase of BaNi$_2$As$_2$.@ Here we show that between the high- and low-$T$ phases of Ba(Ni,Co)$_2$(As,P)$_2$ an additional phase with broken fourfold symmetry and $d_{xz}$ orbital order exists which is a promising candidate for charge-fluctuation-induced nematicity. Moreover, we find evidence that suppression of the (distorted) zig-zag chains by reducing the contribution of the $d_{xy}$ orbitals leads to an enhanced $T_{rm c}$.@