![]() One is that SOC can open a full gap between the highest valence band and the lowest conduction band, and a topological insulating state may emerge, given a proper interaction between M- d and M’- d states (shown in panel c). We conjecture that when spin-orbit coupling (SOC) is included, we can have two situations in which non-trivial topology may emerge. Given a proper combination of M and M’ and their d occupancy, M- d states, and M’- d states may overlap with each other around the Fermi level (shown in panel b). Due to the electronegativity difference, the d orbitals of M have higher energies than the d orbitals of M’. We choose M to be an early transition metal atom and M’ to be a late transition metal atom. We start from the simplest configuration: a (001) ( AMO 3) 1/( AM’O 3) 1 superlattice, in which M and M’ are two different transition metal atoms (shown in panel a of Fig. Therefore, we wonder whether non-trivial topological properties may emerge in (001) oxide superlattices. In particular, those oxides with non-polar terminations and can be accurately controlled on the atomic scale in a layer-by-layer manner in an oxide superlattice. By contrast, (001) perovskite oxide heterostructures have been routinely synthesized. However, (111) terminations of perovskite oxide AMO 3 are polar and it is very difficult to synthesize such films with precise control of their thickness in experiments. Like graphene, the transition metal d-bands form a linear crossing at the high-symmetry K/K’ point in the Brillouin zone and spin-orbit coupling (SOC) opens a gap at the crossing and thus a quantum spin Hall state may emerge. An intriguing proposal is to study a bi-layer of perovskite oxide AMO 3 thin film along (111) direction, in which the transition metal atom M resides on a buckled honeycomb lattice. However, complex oxides with characteristic d orbitals have been less explored. In time-reversal-invariant crystalline solids, topological insulating state and topological metallic state (with Dirac points and/or Dirac node lines) have been intensively studied in narrow-gap semiconductors whose electronic structure is dominated by s and p orbitals. Searching for non-trivial topological states has been one of the most active fields in condensed matter physics and materials science.
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