Exploring topological double-Weyl semimetals with cold atoms in optical lattices

Abstract

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 $pm2$behaveassinkandsourceofBerryfluxinmomentumspaceconnectingbytwoFermiarcsandtheyarestabilizedbythe\$C_{4h}$ point-group symmetry. By applying a realizable $C_4$breakingterm,wefindthateachdouble-Weylpointsplitsintotwosingle-WeylpointsandobtainrichphasediagramsintheparameterspacespannedbythestrengthsofaneffectiveZeemantermandthe\$C_4$ 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 $C_4$ 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.

12 pages, 7 figures; accepted by PRA

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