Abstract
Topological semimetals/metals (TSMs/TMs), as a family of symmetry-protected topological materials, feature nontrivial band crossings near Fermi energy in their electronic band structures, around which fascinating types of emergent fermions (such as Weyl and Dirac fermions or even beyond) appear and promise a range of intriguing physical effects. These band crossings cannot be gapped by band repulsion unless the protecting symmetries are broken or the system undergoes a topological phase transition. A remarkable consequence is that, by means of symmetry and topology, TSMs/TMs can be classified into different categories sharing common characteristics, and this offers guidance toward the discovery of new topological materials. However, a complete classification of TSMs/TMs is still missing due to the complexity of space group symmetries in combination with spin-orbit coupling (SOC), the uncertainty of topological invariants, as well as the diversity of band crossings. Furthermore, the search of suitable candidate materials remains a challenge because of the complicated dispersion in real materials. In this thesis, we explore new classes of symmetry-protected TSMs/TMs, looking for their symmetry condition and topological classification, investigating their topological and physical properties, and searching for suitable materials candidates to facilitate the experimental observation. First, we study the TSMs/TMs possessing massless Dirac fermions with quadratic and cubic dispersions protected by crystallographic symmetries. Several previously unknown classes including chiral quadratic Dirac points with large Chern numbers and extensive surface Fermi arcs, quadratic Dirac points protected by certain magnetic symmetry, and cubic Dirac points without centrosymmetry are found. Then, we generalize the classification based on order of dispersion to TSMs/TMs with nodal lines and provide the symmetry conditions for the quadratic and cubic nodal lines. We further reveal their unique physical properties, such as the (joint) density of states, magneto-response, transport behavior, topological surface states, and topological phase transitions. TSMs/TMs can also be classified according to the dimension of degeneracy manifolds. In three-dimensional (3D) systems, in addition to nodal points and nodal lines, there is one remaining possibility, nodal surfaces, with the band crossing points forming a two-dimensional (2D) surface in the Brillouin zone. We therefore explore different classes of nodal surfaces, both in the absence and in the presence of SOC, and further generalize the result to magnetically ordered systems. Besides the TSMs/TMs in 3D systems, we reveal a type of doubly degenerate iii nodal loops in 2D systems, which is robust against SOC and features an hourglass-type dispersion. Finally, we have identified realistic material candidates for the realization of the above types of TSMs/TMs both in 2D and 3D systems based on first-principles calculations. The work in this thesis not only offers a useful scheme for the classification of TSMs/TMs, and it also constitutes a freshingly new starting point for the further studies of these TSMs/TMs. The predicted materials can be directly explored in experiment, and our proposed symmetry criteria can be easily implemented to search more material candidates in future.