Youngkuk Kim

We propose and characterize a new Z2 class of topological semimetals with a vanishing spin-orbit interaction. The proposed topological semimetals are characterized by the presence of bulk one-dimensional (1D) Dirac line nodes (DLNs) and two-dimensional (2D) nearly flat surface states, protected by inversion and time-reversal symmetries. We develop the Z2 invariants dictating the presence of DLNs based on parity eigenvalues at the parity-invariant points in reciprocal space. Moreover, using first-principles calculations, we predict DLNs to occur in Cu_{3}N near the Fermi energy by doping nonmagnetic transition metal atoms, such as Zn and Pd, with the 2D surface states emerging in the projected interior of the DLNs. This Letter includes a brief discussion of the effects of spin-orbit interactions and symmetry breaking as well as comments on experimental implications.

We study a class of Dirac semimetals that feature an eightfold-degenerate double Dirac point. We show that 7 of the 230 space groups can host such Dirac points and argue that they all generically display linear dispersion. We introduce an explicit tight-binding model for space groups 130 and 135. Space group 135 can host an intrinsic double Dirac semimetal with no additional states at the Fermi energy. This defines a symmetry-protected topological critical point, and we show that a uniaxial compressive strain applied in different directions leads to topologically distinct insulating phases. In addition, the double Dirac semimetal can accommodate topological line defects that bind helical modes. Connections are made to theories of strongly interacting filling-enforced semimetals, and potential materials realizations are discussed.

Higher-order topological insulators are newly proposed topological phases of matter, whose bulk topology manifests as localized modes at two- or higher-dimensional lower boundaries. In this Letter, we propose the twisted bilayer graphenes with large angles as higher-order topological insulators, hosting topological corner charges. At large commensurate angles, the intervalley scattering opens up the bulk gap and the corner states occur at half filling. Based on both first-principles calculations and analytic analysis, we show the striking results that the emergence of the corner states do not depend on the choice of the specific angles as long as the underlying symmetries are intact. Our results show that the twisted bilayer graphene can serve as a robust candidate material of a two-dimensional higher-order topological insulator.

We study the band topology and the associated linking structure of topological semimetals with nodal lines carrying Z_{2} monopole charges, which can be realized in three-dimensional systems invariant under the combination of inversion P and time reversal T when spin-orbit coupling is negligible. In contrast to the well-known PT-symmetric nodal lines protected only by the π Berry phase, in which a single nodal line can exist, the nodal lines with Z_{2} monopole charges should always exist in pairs. We show that a pair of nodal lines with Z_{2} monopole charges is created by a double band inversion process and that the resulting nodal lines are always linked by another nodal line formed between the two topmost occupied bands. It is shown that both the linking structure and the Z_{2} monopole charge are the manifestation of the nontrivial band topology characterized by the second Stiefel-Whitney class, which can be read off from the Wilson loop spectrum. We show that the second Stiefel-Whitney class can serve as a well-defined topological invariant of a PT-invariant two-dimensional insulator in the absence of Berry phase. Based on this, we propose that pair creation and annihilation of nodal lines with Z_{2} monopole charges can mediate a topological phase transition between a normal insulator and a three-dimensional weak Stiefel-Whitney insulator. Moreover, using first-principles calculations, we predict ABC-stacked graphdiyne as a nodal line semimetal (NLSM) with Z_{2} monopole charges having the linking structure. Finally, we develop a formula for computing the second Stiefel-Whitney class based on parity eigenvalues at inversion-invariant momenta, which is used to prove the quantized bulk magnetoelectric response of NLSMs with Z_{2} monopole charges under a T-breaking perturbation.

We review recent theoretical progress in the understanding and prediction of novel topological semimetals. Topological semimetals define a class of gapless electronic phases exhibiting topologically stable crossings of energy bands. Different types of topological semimetals can be distinguished on the basis of the degeneracy of the band crossings, their codimension (e.g., point or line nodes), and the crystal space group symmetries on which the protection of stable band crossings relies. The dispersion near the band crossing is a further discriminating characteristic. These properties give rise to a wide range of distinct semimetal phases such as Dirac or Weyl semimetals, point or line node semimetals, and type I or type II semimetals. In this review we give a general description of various families of topological semimetals, with an emphasis on proposed material realizations from first-principles calculations. The conceptual framework for studying topological gapless electronic phases is reviewed, with a particular focus on the symmetry requirements of energy band crossings, and the relation between the different families of topological semimetals is elucidated. In addition to the paradigmatic Dirac and Weyl semimetals, we pay particular attention to more recent examples of topological semimetals, which include nodal line semimetals, multifold fermion semimetals, and triple-point semimetals. Less emphasis is placed on their surface state properties, their responses to external probes, and recent experimental developments.