Phase stability and large in-plane resistivity anisotropy in the 112-type iron-based superconductor Ca1−xLaxFeAs2

The recently discovered high-${T}_c$ superconductor ${\mathrm{Ca}}_{1\ensuremath{-}x}{\mathrm{La}}_x{\mathrm{FeAs}}₂$ is a unique compound not only because of its low-symmetry crystal structure but also because of its electronic structure, which hosts Dirac-like metallic bands resulting from (spacer) zigzag As chains. We present a comprehensive first-principles theoretical study of the electronic and crystal structures of ${\mathrm{Ca}}_{1\ensuremath{-}x}{\mathrm{La}}_x{\mathrm{FeAs}}₂$. After discussing the connection between the crystal structure of the 112 family, which ${\mathrm{Ca}}_{1\ensuremath{-}x}{\mathrm{La}}_x{\mathrm{FeAs}}₂$ is a member of, with the other known structures of Fe pnictide superconductors, we check the thermodynamic phase stability of ${\mathrm{CaFeAs}}₂$, and similar hyphothetical compounds ${\mathrm{SrFeAs}}₂$ and ${\mathrm{BaFeAs}}₂$ which, we find, are slightly higher in energy. We calculate the optical conductivity of ${\mathrm{Ca}}_{1\ensuremath{-}x}{\mathrm{La}}_x{\mathrm{FeAs}}₂$ using the DFT+DMFT method and predict a large in-plane resistivity anisotropy in the normal phase, which does not originate from electronic nematicity, but is enhanced by the electronic correlations. In particular, we predict a 0.34 eV peak in the $yy$ component of the optical conductivity of the 30% La-doped compound, which corresponds to coherent interband transitions within a fast-dispersing band arising from the zigzag As chains, which are unique to this compound. We also study the Landau free energy for ${\mathrm{Ca}}_{1\ensuremath{-}x}{\mathrm{La}}_x{\mathrm{FeAs}}₂$ including the order parameter relevant for the nematic transition and find that the free energy does not have any extra terms that could induce ferro-orbital order. This explains why the presence of As chains does not broaden the nematic transition in ${\mathrm{Ca}}_{1\ensuremath{-}x}{\mathrm{La}}_x{\mathrm{FeAs}}₂$.