Observation of nodal-line semimetal with ultracold fermions in an optical lattice

Abstract

Observation of topological phases beyond twodimension (2D) has been an open challenge for ultracold atoms. Here, we realize for the first time a 3D spin-orbit coupled nodal-line semimetal in an optical lattice and observe the bulk line nodes with ultracold fermions. The realized topological semimetal exhibits an emergent magnetic group symmetry. This allows to detect the nodal lines by effectively reconstructing the 3D topological band from a series of measurements of integrated spin textures, which precisely render spin textures on the parameter-tuned magnetic-groupsymmetric planes. The detection technique can be generally applied to explore 3D topological states of similar symmetries. Furthermore, we observe the band inversion lines from topological quench dynamics, which are bulk counterparts of Fermi arc states and connect the Dirac points, reconfirming the realized topological band. Our results demonstrate the first approach to effectively observe 3D band topology, and open the way to probe exotic topological physics for ultracold atoms in high dimensions.The past decade has witnessed great progresses in search for topological quantum phases, in particular the topological insulators [1, 2] and semimetals [3][4][5][6][7] in solid state materials which commonly have strong spinorbit (SO) couplings. Among the topological phases, a semimetal phase has gapless bulk nodes protected by symmetry and topology [8,9]. Particularly, the nodalline semimetal has degenerate bulk quasiparticles extending 1D line [10,11], and can serve as a parent phase to further realize exotic states including Weyl semimetals and topological insulators. Unlike the boundary modes of a topological matter which can be resolved with transport measurements or ARPES technique [1,2], the bulk topology is usually harder to detect. For nodal-line semimetals, the line-shape nodes of solids are embedded in the 3D band structure and their direct imaging could be im- * These authors contributed equally to this work. † Electronic address: xiongjunliu@pku.edu.cn ‡ Electronic address: gbjo@ust.hk

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Z2 characterization for three-dimensional multiband Hubbard models

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Detecting Fractional Chern Insulators in Optical Lattices Through Quantized Displacement

“…Introduction.-Ultracold atoms in optical lattices have recently become a fruitful field for the realization of topological states of matter [1][2][3][4][5][6][7][8][9]. The engineering of artificial gauge fields [10,11] has enabled the creation of band structures with nontrivial topology [1,12,13], and their nonzero Chern numbers [2,[14][15][16][17][18] and chiral edge states [19,20] have been detected in the laboratory.…”