  Oxide heterostructures exhibit many intriguing properties. Here we provide
design principles for inducing multiple topological states in (001)
($AM$O$_3$)$_1$/($AM'$O$_3$)$_1$ oxide superlattices. Aided by first-principles
calculations and model analysis, we show that a (Sr$M$O3)$_1$/(Sr$M'$O$_3$)$_1$
superlattice ($M$ = Nb, Ta and $M'$ = Rh, Ir) is a strong topological insulator
with $Z_2$ index (1;001). More remarkably, a (SrMoO3)$_1$/(SrIrO3)$_1$
superlattice exhibits multiple coexisting topological insulator (TI) and
topological Dirac semi-metal (TDS) states. The TDS state has a pair of type-II
Dirac points near the Fermi level and symmetry-protected Dirac node lines. The
surface TDS Dirac cone is sandwiched by two surface TI Dirac cones in the
energy-momentum space. The non-trivial topological properties arise from the
band inversion between $d$ orbitals of two dissimilar transition metal atoms
and a particular parity property of (001) superlattice geometry. Our work
demonstrates how to induce nontrivial topological states in (001) perovskite
oxide heterostructures by rational design.
