  Time-reversal broken Weyl semimetals have attracted much attention recently,
but certain aspects of their behavior, including the evolution of their Fermi
surface topology and anomalous Hall conductivity with Fermi-level position,
have remained underexplored. A promising route to obtain such materials may be
to start with a nonmagnetic Dirac semimetal and break time-reversal symmetry
via magnetic doping or magnetic proximity. Here we explore this scenario in the
case of the Dirac semimetal Cd$_{3}$As$_{2}$, based on first-principles
density-functional calculations and subsequent low-energy modeling of
Cd$_{3}$As$_{2}$ in the presence of a Zeeman field applied along the symmetry
axis. We clarify how each four$-$fold degenerate Dirac node splits into four
Weyl nodes, two with chirality $\pm 1$ and two higher-order nodes with
chirality $\pm 2$. Using a minimal \kdotp model Hamiltonian whose parameters
are fit to the first-principles calculations, we detail the evolution of the
Fermi surfaces and their Chern numbers as the Fermi energy is scanned across
the region of the Weyl nodes at fixed Zeeman field. We also compute the
intrinsic anomalous Hall conductivity as a function of Fermi-level position,
finding a characteristic inverted-dome structure. Cd$_{3}$As$_{2}$ is
especially well suited to such a study because of its high mobility, but the
qualitative behavior revealed here should be applicable to other Dirac
semimetals as well.
