Topological hinge modes in Dirac semimetals

Abstract

Dirac semimetals (DSMs) are an important class of topological states of matter. Here, focusing on DSMs of band inversion type, we investigate their boundary modes from the effective model perspective. We show that in order to properly capture the boundary modes, k-cubic terms must be included in the effective model, which would drive an evolution of surface degeneracy manifold from a nodal line to a nodal point. Sizable k-cubic terms are also needed for better exposing the topological hinge modes in the spectrum. Using first-principles calculations, we demonstrate that this feature and the topological hinge modes can be clearly exhibited in β-CuI. We extend the discussion to magnetic DSMs and show that the time-reversal symmetry breaking can gap out the surface bands and hence is beneficial for the experimental detection of hinge modes. Furthermore, we show that magnetic DSMs serve as a parent state for realizing multiple other higher-order topological phases, including higher-order Weyl-point/nodal-line semimetals and higher-order topological insulators.

Graphical abstract

Keywords

topological / hinge / Dirac / semimetals

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Note added

Recently, a preprint appeared [48], which reported higher-order Dirac semimetal state in the materials Pd{}_3Pb{}_2X{}_2 (X = S, Se).

Acknowledgements

We thank Zhijun Wang and D. L. Deng for helpful discussions. We acknowledge computational support from HPC of Beihang University. This work is supported by the NSFC (Grants No. 12174018, No. 12074024, No. 11774018), the National Key R&D Program of China (No. 2022YFA1402600), the Fundamental Research Funds for the Central Universities and the Singapore Ministry of Education AcRF Tier 2 (MOE-T2EP50220-0011).

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