Symmetry-Indicated Time-Reversal-Doubled Axion Insulators

Abstract

The axion insulator exhibits a topological magnetoelectric effect characterized by an axion angle $\hat{I}¸=\ddot{I}€$, while the time-reversal-doubled axion insulator (T-DAXI) can be viewed as two copies of an axion insulator related by time-reversal symmetry. In this work, we show that a topological crystalline insulator with nonsymmorphic glide or screw symmetry hosts the T-DAXI phase. The spin-resolved topology of the T-DAXI phase is guaranteed by the nonsymmorphic symmetry invariant $\hat{I}{´}_g=1$ or $\hat{I}{´}_s=1$ in certain spin directions. In this phase, the partial axion angles are quantized to $\ddot{I}€$, and the gapped surfaces realize half-quantized quantum spin Hall states. By applying an external magnetic field along the $z$ direction, electrons with opposite spins accumulate on opposite $(001)$ surfaces, producing a topological spin polarization in real space. When the magnetic field is time-periodic, this leads to an alternating spin current detectable in experiment. Using $\text{ab initio}$ calculations, we demonstrate that mixed bismuth monohalides Bi4Br3I and Bi4BrI3 realize the nonsymmorphic T-DAXI with $\hat{I}{´}_g=\hat{I}{´}_s=1$. Our findings not only reveal the symmetry-enforced T-DAXIs in nonsymmorphic topological crystalline insulators, but also introduce the spin magnetoelectric effect as a novel topological spin response.

8 pages, 5 figures, 1 table