  Recent studies have predicted that magnetic EuCd2As2 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 non-magnetic analogs AECd2As2 (AE = Ca,
Sr, Ba) as studied with density functional theory calculations. Under ambient
pressure we find 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
anti-bonding state derived mostly from Cd 5s orbitals. The combination of these
two competing effects results in a non-monotonic change of the band gap size
across the AE series with SrCd2As2 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
${\Gamma}$-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
(10-10) surface.
