Pressure effect on band inversion in A E Cd 2 As 2 ( A E = Ca , Sr , Ba )

Recent studies have predicted that magnetic ${\mathrm{EuCd}}_{2}{\mathrm{As}}_{2}$ can host several different topological states depending on its magnetic order, including a single pair of Weyl points. Here we report on the bulk properties and band inversion induced by pressure in the nonmagnetic analogs $AE{\mathrm{Cd}}_{2}{\mathrm{As}}_{2}$ $(AE=\mathrm{Ca}, \mathrm{Sr}, \mathrm{Ba})$ as studied with density functional theory calculations. Under ambient pressure we find that these compounds are narrow band gap semiconductors, in agreement with experiment. The size of the band gap is dictated by both the increasing ionicity across the AE series which tends to increase the band gap, as well as the larger nearest neighbor Cd-As distance from increasing atomic size which can decrease the band gap because the conduction band edge is an antibonding state derived mostly from Cd $5s$ orbitals. The combination of these two competing effects results in a nonmonotonic change of the band gap size across the AE series with ${\mathrm{SrCd}}_{2}{\mathrm{As}}_{2}$ having the smallest band gap among the three compounds. The application of negative pressure reduces this band gap and causes the band inversion between the Cd $5s$ and As $4p$ orbitals along the $\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}A$ direction to induce a pair of Dirac points. The topological nature of the Dirac points is then confirmed by finding the closed Fermi arcs on the $(10\overline{1}0)$ surface.