The discovery of topological quantum states has attracted abundant interest in recent years in the field of condensed matter physics. The reason behind is that the corresponding exotic quantum transport properties are expected to be useful in future electronic and spintronic devices. This thesis focuses on the studies and predictions of different topological materials using first-principles calculations and symmetry analysis, with special focuses on magnetic topological materials and topological phononic materials.

In the first project, using first-principles calculations, we found that three-dimensional quantum anomalous Hall effect can be realized in a family of intrinsic ferromagnetic insulating oxides, including layered and nonlayered compounds that share a centrosymmetric structu...[ Read more ]

The discovery of topological quantum states has attracted abundant interest in recent years in the field of condensed matter physics. The reason behind is that the corresponding exotic quantum transport properties are expected to be useful in future electronic and spintronic devices. This thesis focuses on the studies and predictions of different topological materials using first-principles calculations and symmetry analysis, with special focuses on magnetic topological materials and topological phononic materials.

In the first project, using first-principles calculations, we found that three-dimensional quantum anomalous Hall effect can be realized in a family of intrinsic ferromagnetic insulating oxides, including layered and nonlayered compounds that share a centrosymmetric structure with space group R3̅m. The Hall conductivity is quantized to be −3e²/ℎc with the lattice constant c along the c axis. The chiral surface sheet states are clearly visible and uniquely distributed on the surfaces that are parallel to the magnetic moment.

In the second project, we presented an inversion eigenvalue argument to dictate the existence of even pairs of ferromagnetic Weyl fermions. We showed, by a combination of first-principles calculations and symmetry analyses, that this exotic topological feature can be verified in ferromagnetic oxides in different space groups. In particular, a realistic candidate, i.e., hollandite RbCr₄O₈ with a high Curie temperature (∼295 K), hosts intriguing twin pairs of Weyl fermions, which are robustly stable against perturbations. Moreover, our effective model and symmetry analysis showed that the twin pairs of Weyl fermions originate from a mirrored nodal ring pair. The nontrivial surface states and Fermi arcs of RbCr₄O₈ are clearly visible, further revealing the topological features.

In the third project, we showed by first-principles calculations and symmetry analysis that ideal type-II Weyl phonons are present in zinc-blende cadmium telluride, a well-known II-VI semiconductor. Importantly, these type-II Weyl phonons originate from the inversion between the longitudinal acoustic and transverse optical branches. Symmetry guarantees that the type-II Weyl points lie along the high-symmetry lines at the boundaries of the Brillouin zone even with a breaking of inversion symmetry, exhibiting the robustness of protected phonon features.

In the fourth project, we proposed a strategy to explore and design materials that can realize the type-III nodal-ring phonons by introducing two-dimensional (2D) lattices with ideal flat band. As a concrete example, we showed by first-principles calculations that the Laves phase AB₂ with C14 structure possesses ideal type-III nodal-ring phonons. The flat phonon band related to type-III nodal-ring phonons originates from their 2D triangular and kagome layers in the Laves phase AB₂. The type-III nodal-ring phonons with nontrivial Berry phase lie on a reflection-invariant plane, which are protected by the inversion and time-reversal symmetries. In addition, the drumhead surface states and unique surface arcs are clearly visible, which facilitate experimental observations.

In summary, using first-principles calculations and symmetry analysis, we investigated a wide range of nontrivial topological states in materials from electronic materials to phononic materials. Our study may contribute to the development of topological materials.