Time-reversal-breaking topological phases in antiferromagnetic ${\mathrm{Sr}}_2{\mathrm{FeOsO}}_6$ films

In this work, we studied time-reversal-breaking topological phases as a result of the interplay between antiferromagnetism and inverted band structures in antiferromagnetic double perovskite transition-metal ${\mathrm{Sr}}_2{\mathrm{FeOsO}}_6$ films. By combining the first-principles calculations and analytical models, we demonstrate that the quantum anomalous Hall phase and chiral topological superconducting phase can be realized in this system. We find that to achieve time-reversal-breaking topological phases in antiferromagnetic materials, it is essential to break the combined symmetry of time reversal and inversion, which generally exists in antiferromagnetic structures. As a result, we can utilize an external electric gate voltage to induce the phase transition between topological phases and trivial phases, thus providing an electrically controllable topological platform for future transport experiments.

Figure 1

(a) The crystal structure of ${\mathrm{Sr}}_2{\mathrm{FeOsO}}_6$. One tetragonal unit cell is shown, where the Sr atoms are omitted for simplicity. (b) Schematic plot of the bilayer film with gate voltage $U_{\mathrm{A}}$. The arrows on the atoms denote the local magnetic moments. The substrate could be a normal insulator or an $s$-wave superconductor.

Figure 2

The band structure of the bilayer film with (a) $U_{\mathrm{A}}=0$ eV, (b) $-0.03$ eV, (c) $-0.246$ eV, and (d) $-0.3$ eV. (e) The density of states on one edge of a ribbon configuration along the $x$ direction with $U_{\mathrm{A}}=-0.3$ eV. Two insets are the zoom-in of the corresponding regions.

Figure 3

(a) The dispersion of the BdG Hamiltonian of the bilayer system with $U_{\mathrm{A}}=-0.01$ eV and $\mu =-0.18$ eV. (b) The edge dispersion in a 1D ribbon configuration along the $x$ direction with the same parameters as in (a). Correspondingly, the parameters in (c) and (d) are $U_{\mathrm{A}}=-0.05$ eV and $\mu =-0.21$ eV, and in (e) and (f) are $U_{\mathrm{A}}=-0.01$ eV and $\mu =-0.24$ eV. The value of $\mathrm{\Delta }$ is fixed at 0.015 eV in all these figures.

Figure 4

(a) Phase diagram of the CTSC phases in the region $-0.06<U_{\mathrm{A}}<0.06$ eV and $-0.27<\mu <-0.16$ eV. The dark lines are phase boundaries. The number in each phase denotes the corresponding chirality. The value of $\mathrm{\Delta }$ is fixed at 0.015 eV.

Figure 5

Band-structure comparison between few low-energy bands, keeping only Fe-$d$ and Os-$t_{2g}$ orbitals in the Wannier basis (light dotted line) and full DFT bands (black continuous line) calculated using $\mathrm{GGA}+U_{\mathrm{eff}}$ in the antiferromagnetic configurations. $U_{\mathrm{eff}}^{\mathrm{Fe}}=4$ eV and $U_{\mathrm{eff}}^{\mathrm{Os}}=2$ eV were used for evaluating the low-energy Hamiltonian.

Figure 6

The original BZ and the reduced BZ (enclosed by dashed lines) when there is a CDW or SDW term. Region A will move to region B during the BZ folding process.

Figure 7

The energy bands in the reduced BZ with different gate voltage $U_{\mathrm{A}}$ (the values in each figure). The blue and red lines in (a), (c), (e), and (g) are the bands without a CDW or SDW term. The black lines in (b), (d), (f), and (h) are the bands with a CDW or SDW term.

Figure 8

The density of states on one edge of a ribbon configuration along the $x$ direction of a four-layer film. The effective electric potential on the top layer is $-0.23$ eV and on the bottom layer is 0.23 eV.