Universal momentum-to-real-space mapping of topological singularities

Xiuying Liu, Shiqi Xia, Ema Jajtić, Daohong Song (), Denghui Li, Liqin Tang, Daniel Leykam, Jingjun Xu, Hrvoje Buljan () and Zhigang Chen ()
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Xiuying Liu: Nankai University
Shiqi Xia: Nankai University
Ema Jajtić: University of Zagreb
Daohong Song: Nankai University
Denghui Li: Nankai University
Liqin Tang: Nankai University
Daniel Leykam: Center for Theoretical Physics of Complex Systems, Institute for Basic Science
Jingjun Xu: Nankai University
Hrvoje Buljan: Nankai University
Zhigang Chen: Nankai University

Nature Communications, 2020, vol. 11, issue 1, 1-8

Abstract: Abstract Topological properties of materials are typically presented in momentum space. Here, we demonstrate a universal mapping of topological singularities from momentum to real space. By exciting Dirac-like cones in photonic honeycomb (pseudospin-1/2) and Lieb (pseudospin-1) lattices with vortex beams of topological charge l, optimally aligned with a given pseudospin state s, we directly observe topological charge conversion that follows the rule l → l + 2s. Although the mapping is observed in photonic lattices where pseudospin-orbit interaction takes place, we generalize the theory to show it is the nontrivial Berry phase winding that accounts for the conversion which persists even in systems where angular momentum is not conserved, unveiling its topological origin. Our results have direct impact on other branches of physics and material sciences beyond the 2D photonic platform: equivalent mapping occurs for 3D topological singularities such as Dirac-Weyl synthetic monopoles, achievable in mechanical, acoustic, or ultracold atomic systems, and even with electron beams.

Date: 2020
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DOI: 10.1038/s41467-020-15374-x

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