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arXiv:2003.03561 · Physical Review A

Simulation of a nodal-line semimetal in amplitude-shaken optical lattices

Tan-Ji Zhou, Zhongcheng Yu, Zhihan Li, Xuzong Chen, Xiaoji Zhou

Published Aug 26, 2020• 2 citations
arXivHTMLPDF

Abstract

As the research of topological semimetals develops, semimetals with nodal-line rings have come into people's vision as a new platform for studying electronic topology. We propose a method that uses ultracold atoms in a two-dimensional amplitude-shaken bipartite hexagonal optical lattice to simulate the nodal-line semimetal, which can be achieved in the experiment by attaching one triangular optical lattice to a hexagonal optical lattice and periodically modulating the intensity and position of the triangular lattice. By adjusting the shaking frequency and well depth difference of the hexagonal optical lattice, a transformation from Dirac semimetal to the nodal-line semimetal is observed in our system. This transformation can be demonstrated by the Berry phase and Berry curvature, which guides the measurement. Furthermore, the amplitude shaking and ${C}_{3}$ symmetry generate a time-reversal-symmetry-unstable mode, and the proportion of the mode and the trivial mode of the hexagonal lattice controls the transformation. This proposal paves a way to study nodal-line semimetals in two-dimensional systems, and it contributes to the application of nodal-line semimetals.

DOI
10.1103/physreva.102.023328

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As the research of topological semimetals develops, semimetals with nodal-line rings have come into people's vision as a new platform for studying electronic topology. We propose a method that uses ultracold atoms in a two-dimensional amplitude-shaken bipartite hexagonal optical lattice to simulate the nodal-line semimetal, which can be achieved in the experiment by attaching one triangular optical lattice to a hexagonal optical lattice and periodically modulating the intensity and position of the triangular lattice. By adjusting the shaking frequency and well depth difference of the hexagonal optical lattice, a transformation from Dirac semimetal to the nodal-line semimetal is observed in our system. This transformation can be demonstrated by the Berry phase and Berry curvature, which guides the measurement. Furthermore, the amplitude shaking and C3{C}_{3}C3​ symmetry generate a time-reversal-symmetry-unstable mode, and the proportion of the mode and the trivial mode of the hexagonal lattice controls the transformation. This proposal paves a way to study nodal-line semimetals in two-dimensional systems, and it contributes to the application of nodal-line semimetals.
Despite recent breakthroughs in topological bands for ultracold atoms in 1D and 2D, it has been an open challenge to realize and observe 3D topological matter in an atomic system. While numerous schemes have been proposed, the experimental complexity and the characterization of the 3D band structure acted as a barrier against experimental groups achieving this outstanding goal. In this talk, we report the realization and observation of 3D nodal-line semimetal band with spin-orbit-coupled ultracold fermions. The 3D topological band structure is achieved by stacking 2D Dirac semimetal in the x-y plane along z direction in Raman-dressed optical lattices. To detect 3D topological phases, we developed kz resolved spin texture measurement technique based on emergent magnetic group symmetry in our system. By directly imaging spin texture in specific kz plane with different Zeeman splitting, 3D nodal lines can be reconstructed. The realization of topological band structure is also verified in quench dynamics by detecting band inversion lines, which are bulk counterparts of Fermi arc states. This technique can be broadly applied to characterizing 3D topological states with similar symmetries.
Exploring 3D topological matter with spin-orbit-coupled fermions in optical lattices1 CHENGDONG HE, BO SONG, Hong Kong University of Science and Technology, SEN NIU, LONG ZHANG, Peking University, ZEJIAN REN, ENTONG ZHAO, Hong Kong University of Science and Technology, XIONG-JUN LIU, Peking University, GYU-BOONG JO, Hong Kong University of Science and Technology — Ultracold atoms offer a promising testbed for the experimental study of topological matter. Various topological models have been recently realized in 1D and 2D atomic systems. While 3D topological matter with rich physics remains unexplored due to experimental complexity. Here we report, for the first time, the realization of a 3D nodal line semimetal in optical lattices with SO coupled ultracold fermions. The 3D topological band structure is achieved by stacking 2D Dirac semimetal in the x-y plane along z direction in Raman-dressed optical lattices. kz resolved spin texture measurement technique based on emergent magnetic group symmetry has been developed to detect 3D topological state. Spin texture in a specific kz plane can be directly imaged with different Zeeman splitting. 3D nodal lines can be reconstructed with this pseudo-tomography method. Band inversion lines, the bulk counterparts of Fermi arc states, can be extracted from quench dynamics, which reconfirmed the realization of topological phase. Our detection technique can be broadly applied to characterizing 3D topological states with similar symmetries, which provides a new possibility to study exotic quantum physics in higher dimensions.
We point out that a face-centered-cubic (fcc) optical lattice, which can be realized by a simple scheme using three lasers, provides one a highly controllable platform for creating Weyl points and topological nodal superfluids in ultracold atoms. In noninteracting systems, Weyl points automatically arise in the Floquet band structure when shaking such fcc lattices, and sophisticated design of the tunneling is not required. More interestingly, in the presence of attractive interaction between two hyperfine spin states, which experience the same shaken fcc lattice, a three-dimensional topological nodal superfluid emerges, and Weyl points show up as the gapless points in the quasiparticle spectrum. One could either create a double Weyl point of charge 2, or split it into two Weyl points of charge 1, which can be moved in the momentum space by tuning the interactions. Correspondingly, the Fermi arcs at the surface may be linked with each other or separated as individual ones.
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We propose that a tunable generalized three-dimensional Hofstadter Hamiltonian can be realized by engineering the Raman-assisted hopping of ultracold atoms in a cubic optical lattice. The Hamiltonian describes a periodic lattice system under artificial magnetic fluxes in three dimensions. For certain hopping configurations, the bulk bands can have Weyl points and nodal loops, respectively, allowing the study of both the two nodal semimetal states within this system. Furthermore, we illustrate that with proper rational fluxes and hopping parameters, the system can exhibit the three-dimensional quantum Hall effect when the Fermi level lies in the band gaps, which is topologically characterized by one or two nonzero Chern numbers. Our proposed optical-lattice system provides a promising platform for exploring various exotic topological phases in three dimensions.
We explore the topological properties of double-Weyl semimetals with cold atoms in optical lattices. We first propose 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 $\ifmmode\pm\else\textpm\fi{}2$ behave as the sink and source of Berry flux in momentum space connecting by two Fermi arcs and they are stabilized by the C4h{C}_{4h}C4h​ point-group symmetry. By applying a realizable C4{C}_{4}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{C}_{4}C4​ breaking term, which contains a topological and a normal insulating phase 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 time-of-flight imaging; (iii) the band topology of the C4{C}_{4}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.