摘要
Knots and links are fascinating and intricate topological objects.Their influence spans from DNA and molecular chemistry to vortices in superfluid helium,defects in liquid crystals and cosmic strings in the early universe.Here we find that knotted structures also exist in a peculiar class of three-dimensional topological insulators—the Hopf insulators.In particular,we demonstrate that the momentum-space spin textures of Hopf insulators are twisted in a nontrivial way,which implies the presence of various knot and link structures.We further illustrate that the knots and nontrivial spin textures can be probed via standard time-of-flight images in cold atoms as preimage contours of spin orientations in stereographic coordinates.The extracted Hopf invariants,knots,and links are validated to be robust to typical experimental imperfections.Our work establishes the existence of knotted structures in Hopf insulators,which may have potential applications in spintronics and quantum information processing.
作者
Dong-Ling Deng
Sheng-Tao Wang
Kai Sun
L.-M.Duan
邓东灵;王胜涛;孙锴;段路明(Department of Physics,University of Michigan,Ann Arbor,Michigan 48109,USA;Condensed Matter Theory Center and Joint Quantum Institute,Department of Physics,University of Maryland,College Park,MD 20742-4111,USA;Center for Quantum Information,IIIS,Tsinghua University,Beijing 100084;Department of Physics,Harvard University,Cambridge,Massachusetts 02138,USA)
基金
supported by the ARL,the IARPA Logi Q program,and the AFOSR MURI program
supported by Tsinghua University for their visits
the support from NSF under Grant No.PHY1402971.
supported by JQI-NSF-PFC and LPS-MPO-CMTC at the final stage of this paper
