1. School of Physics, Beihang University, Beijing 100191, China 2. Department of Physics, The University of Hong Kong, Hong Kong, China 3. Peng Huanwu Collaborative Center for Research and Education, Beihang University, Beijing 100191, China 4. Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore 5. Center for Quantum Transport and Thermal Energy Science, School of Physics and Technology, Nanjing Normal University, Nanjing 210023, China
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.
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