We explore the topological properties of double-Weyl semimetals with cold atoms in optical lattices. We first propose to realize a tight-binding model of simulating the double-Weyl semimetal with a pair of double-Weyl points by engineering the atomic hopping in a three-dimensional optical lattice. We show that the double-Weyl points with topological charges of ±2 behave as sink and source of Berry flux in momentum space connecting by two Fermi arcs and they are stabilized by the C 4h point-group symmetry. By applying a realizable C4 breaking term, we find that each double-Weyl point splits into two single-Weyl points and obtain rich phase diagrams in the parameter space spanned by the strengths of an effective Zeeman term and the C4 breaking term, which contains a topological and a normal insulating phases and two topological Weyl semimetal phases with eight and four single-Weyl points, apart from the double-Weyl semimetal phase. Furthermore, we demonstrate with numerical simulations that (i) the mimicked double-and single-Weyl points can be detected by measuring the atomic transfer fractions after a Bloch oscillation; (ii) the Chern number of different quantum phases in the phase diagram can be extracted from the center shift of the hybrid Wannier functions, which can be directly measured with the time-of-flight imaging; (iii) the band topology of the C4-symmetric Bloch Hamiltonian can be detected simply from measuring the spin polarization at the high symmetry momentum points with a condensate in the optical lattice. The proposed system would provide a promising platform for elaborating the intrinsic exotic physics of double-Weyl semimetals and the related topological phase transitions.
Novel fermionic quasiparticles with integer pseudospins in some energy bands, such as pseudospin-1 triple-point fermions, recently attract increasing interest since they are beyond the conventional spin-1/2 Dirac and Weyl counterparts. In this paper, we propose a class of pseudospin-1 fermioic excitations emerging in topological metal bands, dubbed double-triple-point (DTP) fermions. We first present a general three-band continuum model with C4 symmetry in three dimensions, which has three types of threefold degenerate points in the bands classified by their topological charges C = ±4, ±2, 0, respectively. They are dubbed DTPs as spin-1 generalization of double-Weyl points. We then construct two-dimensional and three-dimensional tight-binding lattice models of topological metal bands with exotic DTP fermions near the DTPs. In two dimensions, the band gaps close at a trivial DTP with zero Berry phase, which occurs at the transition between the normal and topological insulator phases. In three dimensions, the topological properties of three different DTP fermions in lattice systems are further investigated, and the effects of breaking C4 symmetry are also studied, which generally leads to splitting each quadratic DTP into two linear triple points and gives topological phase diagrams. Using ultracold fermionic atoms in optical lattices, the proposed models can be realized and the topological properties of the DTP fermions can be detected. * Electronic address: danweizhang@m.scnu.edu.cn † Electronic address: slzhu@nju.edu.cn arXiv:1810.11560v1 [cond-mat.quant-gas]
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