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    Stiefel-Whitney classes and topological phases in band theory
    Junyeong Ahn, Sungjoon Park, Dongwook Kim, Youngkuk Kim, Bohm-Jung Yang
    Chin. Phys. B, 2019, 28 (11): 117101.   DOI: 10.1088/1674-1056/ab4d3b
    Abstract1019)   HTML    PDF (4427KB)(473)      
    We review the recent progress in the study of topological phases in systems with space-time inversion symmetry IST. IST is an anti-unitary symmetry which is local in momentum space and satisfies IST2=1 such as PT in two dimensions (2D) and three dimensions (3D) without spin-orbit coupling and C2T in 2D with or without spin-orbit coupling, where P, T, C2 indicate the inversion, time-reversal, and two-fold rotation symmetries, respectively. Under IST, the Hamiltonian and the periodic part of the Bloch wave function can be constrained to be real-valued, which makes the Berry curvature and the Chern number vanish. In this class of systems, gapped band structures of real wave functions can be topologically distinguished by the Stiefel-Whitney numbers instead. The first and second Stiefel-Whitney numbers w1 and w2, respectively, are the corresponding invariants in 1D and 2D, which are equivalent to the quantized Berry phase and the Z2 monopole charge, respectively. We first describe the topological phases characterized by the first Stiefel-Whitney number, including 1D topological insulators with quantized charge polarization, 2D Dirac semimetals, and 3D nodal line semimetals. Next we review how the second Stiefel-Whitney class characterizes the 3D nodal line semimetals carrying a Z2 monopole charge. In particular, we explain how the second Stiefel-Whitney number w2, the Z2 monopole charge, and the linking number between nodal lines are related. Finally, we review the properties of 2D and 3D topological insulators characterized by the nontrivial second Stiefel Whitney class.
    Topology of triple-point metals
    Georg W. Winkler, Sobhit Singh, Alexey A. Soluyanov
    Chin. Phys. B, 2019, 28 (7): 077303.   DOI: 10.1088/1674-1056/28/7/077303
    Abstract772)   HTML    PDF (4289KB)(478)      

    We discuss and illustrate the appearance of topological fermions and bosons in triple-point metals where a band crossing of three electronic bands occurs close to the Fermi level. Topological bosons appear in the phonon spectrum of certain triple-point metals, depending on the mass of atoms that form the binary triple-point metal. We first provide a classification of possible triple-point electronic topological phases possible in crystalline compounds and discuss the consequences of these topological phases, seen in Fermi arcs, topological Lifshitz transitions, and transport anomalies. Then we show how the topological phase of phonon modes can be extracted and proven for relevant compounds. Finally, we show how the interplay of electronic and phononic topologies in triple-point metals puts these metallic materials into the list of the most efficient metallic thermoelectrics known to date.