Strain-induced topological transition in ${\mathrm{SrRu}}_2{\mathrm{O}}_6$ and ${\mathrm{CaOs}}_2{\mathrm{O}}_6$

The topological property of ${\mathrm{SrRu}}_2{\mathrm{O}}_6$ and isostructural ${\mathrm{CaOs}}_2{\mathrm{O}}_6$ under various strain conditions is investigated using density functional theory. Based on an analysis of parity eigenvalues, we anticipate that a three-dimensional strong topological insulating state should be realized when band inversion is induced at the A point in the hexagonal Brillouin zone. For ${\mathrm{SrRu}}_2{\mathrm{O}}_6$, such a transition requires rather unrealistic tuning, where only the $c$ axis is reduced while other structural parameters are unchanged. However, given the larger spin-orbit coupling and smaller lattice constants in ${\mathrm{CaOs}}_2{\mathrm{O}}_6$, the desired topological transition does occur under uniform compressive strain. Our study paves a way to realize a topological insulating state in a complex oxide, which has not been experimentally demonstrated so far.

Figure 1

(a) Top and (b) side views of ${\mathrm{SrRu}}_2{\mathrm{O}}_6$. The cell is doubled along all the directions.

Figure 2

Theoretical phase diagram of ${\mathrm{CaOs}}_2{\mathrm{O}}_6$ under various compressive strains.

Figure 3

GGA+SOC band structure of ${\mathrm{SrRu}}_2{\mathrm{O}}_6$ (a) without applying pressure and (b) under the uniaxial strain by which the $c\text{-axis}$ lattice constant is compressed by 20% while the $a$ and $b$ lattice constants and fractional coordinates are unchanged. The Fermi level is set to $E=0$. Signs $(\pm )$ indicate the parity eigenvalue of the nearly degenerate highest occupied states and the lowest unoccupied state at the A point and that of the occupied states at the other TRIM. In (a), the band topology is trivial, while in (b) it is nontrivial because of the band inversion at the A point. The inset shows the first Brillouin zone.

Figure 4

Band structure of bulk ${\mathrm{CaOs}}_2{\mathrm{O}}_6$ under various strain. (a) Unstrained, (b) 10% compressed along the $c$ axis, (c) 10% compressed along the $ab$ axes, and uniformly compressed along all the direction by (d) 8%, (e) 10%, and (f) 12%. The Fermi level is set to $E=0$. In (a) and (e), results without the SOC are also plotted as short-dashed lines.

Figure 5

Band structure of finite thick slab of ${\mathrm{CaOs}}_2{\mathrm{O}}_6$ with the [001] surface. (a) Unstrained slab and (b) strained slab, which is magnified in (c). The Fermi level is set to $E=0$. The inset shows the surface Brillouin zone.