Doubled Quantum Spin Hall Effect with High-Spin Chern Number in $α$-Antimonene and $α$-Bismuthene

The discovery of quantum spin Hall effect has ignited the field of topological physics with vast variety of exotic properties. Here, we present the emergence of doubled quantum spin Hall effect in two dimensions characterized with a high spin Chern number of ${\mathcal C_S}=2$ and two pairs of helical edge states. Although is overlooked and invisible in topological quantum chemistry and symmetry indicator theory, the already experimentally synthesized $α$-antimonene and $α$-bismuthene are revealed as realistic material candidates of predicted topological states with band inversions emerging at generic $k$-points, rather than the high-symmetry momenta. Remarkably, the nontrivial energy gap can be as large as 464 meV for $α$-bismuthene, indicating the high possibility of room-temperature observation of the doubled quantum spin Hall effect. Moreover, a four-band effective model is constructed to demonstrate further the feasibility of attaining this type of nontrivial topology. Our results not only uncover a novel topological character of antimony and bismuth, but will also facilitate the experimental characterization of the previously overlooked hidden topology.

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