Investigation on topological materials by first-principles calculations

Topological materials characterized by invariant numbers, exhibit novel properties, e.g., symmetry protected surface states, quantized conductivity, chiral anomaly, negative magnetoresistance, etc. It shows that the interplay between symmetry and topology can help us to understand the properties of band topology and enrich the topological classification. The present thesis will start from the development of Hall family and band topology, and then mainly focus on identifying various topological phases in realistic materials, which include the band topology in electronic band structures and phonon spectra. First, based on the tight-binding model and k·p effective Hamiltonian, the four-fold Dirac points are identified to exist in an inversion symmetry breaking system. Such topological phase has nonzero Berry curvature near the crossing nodes, and two edge states connecting one pair of Dirac points. In addition, a family of two-dimensional materials are predicted to host such Dirac points by first-principles calculations, thus facilitate their experimental observations. These findings provide promising avenues to observe exotic transport phenomena beyond graphene, e.g., nonlinear Hall effect. For the topological phonons, a realistic carbon allotropic phase with a body-centered cubic structure termed as bcc-C8 is identified to host ideal nodal ring phonons. Symmetry arguments and effective model show that there are three intersecting phonon nodal rings perpendicular to each other in three different planes. The intersecting phonon nodal rings with quantized Berry phase π are protected by parity_x0002_time symmetry. The hallmark of nodal ring phonons, nearly flat drumhead surface states, are clearly visible on semi-infinite (001) and (110) surfaces. The bcc-C8 can be as ideal candidate for exploring topological nodal ring phonons different from fermionic electrons in other carbon allotropic phases. The chiral quasiparticles with high Chern numbers C usually require extra crystalline symmetries to protect themselves. It means that such quasiparticles is sensitive to symmetry breaking. The three-dimensional irreducible representations of chiral point groups, O(432) and T(23), are verified to host spin-1 Weyl phonons (C = ±2). It further proves that if symmetry breaking decomposes three-dimensional irreducible representations into two-dimensional irreducible representations, the spin-1 Weyl phonons is certainly split into quadratic Weyl phonons (C = ±2). First-principles calculations are applied to identify the splitting mechanisms. The Berry curvature distribution and nontrivial surface states affected by symmetry breaking are obtained in realistic materials. This work builds the connection between different double Weyl phonons and provides guidance for investigating the splitting behavior among other high Chern number quasiparticles.