Title: Rotational symmetry breaking at the incommensurate charge-density-wave transition in Ba(Ni,Co)$_2$(As,P)$_2$: Possible nematic phase induced by charge/orbital fluctuations

Abstract: 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 orthorhombic low-$T$ phase, a unidirectional charge density wave together with (distorted) zig-zag chains are observed for the triclinic 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/orbital-fluctuation-induced nematicity. Moreover, our data suggest that the enhanced $T_{\rm c}$ found for Ba(Ni,Co)$_2$(As,P)$_2$ for higher Co or P substitution levels might result from suppression of the (distorted) zig-zag chains by reducing the contribution of the $d_{xy}$ orbitals.