Fig. 1. (a) Structure of Co$_2$N$_2$ dimer. (b) Structure of Co$_2$N$_2$ layer. The dashed black lines show the mirror symmetries. $X, Y$ coordinates are defined according to the direction of the Co–Co bond, and $x, y$ are the global coordinates in the conventional crystal structure.
Fig. 2. Sketch of intra-orbital NN hopping between anti-bonding molecular orbitals of Co$_2$N$_2$ dimers. The intra-anti-bonding-orbital hoppings between the $d_{X^2-Y^2}^{\rm A}/d_{XZ}^{\rm A}$ molecular orbitals of two NN dimers are forbidden due to the opposite mirror symmetry eigenvalues while those between the $d_{XY}^{\rm A}/d_{YZ}^{\rm A}$ molecular orbitals are allowed.
Specifically, the subscripts $XZ$ and $YZ$ in mirror symmetries $m_{_{\scriptstyle XZ}}$ and $m_{_{\scriptstyle YZ}}$ in Figs. 1 and 2 should be in upper case, instead of $xz$ and $yz$, as they are defined in the local $X$–$Y$ coordinate system.
References