Realization of a two-dimensional Weyl semimetal and topological Fermi strings

Article https://doi.org/10.1038/s41467-024-50329-6 Realization of a two-dimensional Weyl semimetal and topological Fermi strings Received: 26 April 2024 Accepted: 5 July 2024 1234567890():,; 1234567890():,; Check for updates Qiangsheng Lu1,2,13, P. V. Sreenivasa Reddy 3,13, Hoyeon Jeon 4,13, Alessandro R. Mazza2,5, Matthew Brahlek 2, Weikang Wu 6, Shengyuan A. Yang6, Jacob Cook1, Clayton Conner1, Xiaoqian Zhang1, Amarnath Chakraborty1, Yueh-Ting Yao3, Hung-Ju Tien 3, Chun-Han Tseng3, Po-Yuan Yang3, Shang-Wei Lien3, Hsin Lin 7, Tai-Chang Chiang 8,9, Giovanni Vignale 1, An-Ping Li 4 , Tay-Rong Chang 3,10,11 , Rob G. Moore 2 & Guang Bian 1,12 A two-dimensional (2D) Weyl semimetal, akin to a spinful variant of graphene, represents a topological matter characterized by Weyl fermion-like quasiparticles in low dimensions. The spinful linear band structure in two dimensions gives rise to distinctive topological properties, accompanied by the emergence of Fermi string edge states. We report the experimental realization of a 2D Weyl semimetal, bismuthene monolayer grown on SnS(Se) substrates. Using spin and angle-resolved photoemission and scanning tunneling spectroscopies, we directly observe spin-polarized Weyl cones, Weyl nodes, and Fermi strings, providing consistent evidence of their inherent topological characteristics. Our work opens the door for the experimental study of Weyl fermions in low-dimensional materials. The discovery of Weyl semimetals, which host spin-split massless quasiparticles in three-dimensional (3D) crystals, is particularly thrilling as it represents an experimental realization of Weyl fermions, a concept proposed long ago in the realm of particle physics1–5. The chiral nodal points and 2D Fermi arc surface states of 3D Weyl semimetals bring about exotic properties such as chiral anomaly, unusual optical conductivity and nonlocal transport6–16. While the Weyl equation was derived only for odd spatial dimensions, the generalization of a 3D Weyl fermion state in 2D leads to a distinct topological state of matter, labeled as 2D Weyl semimetals, that exhibit a spin-polarized analog of graphene. The dimension reduction gives rise to a multitude of unconventional physical properties, including parity anomaly in (2 + 1)-D (space-time) quantum field theory17–20, charge fractionalization with zero modes of charge e/221, spin-valley Hall effects22,23, giant Berry curvature dipole (BCD)24,25, and topological quantum criticality22. Among the various topological Dirac/Weyl solid-state materials (see Fig. 1a), 2D Weyl semimetals stand out as the final frontier that has yet to be extensively explored in experiments. A winding number of π can be obtained by integrating the Berry phase along a loop encircling each Weyl node26. The nonzero winding number can be regarded as the topological charge of 2D Weyl semimetals, which guarantees the 1 Department of Physics and Astronomy, University of Missouri, Columbia, MO 65211, USA. 2Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA. 3Department of Physics, National Cheng Kung University, Tainan 701, Taiwan. 4Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA. 5Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. 6Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore. 7 Institute of Physics, Academia Sinica, Taipei 11529, Taiwan. 8Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801-3080, USA. 9Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, 104 South Goodwin Avenue, Urbana, IL 61801-2902, USA. 10Center for Quantum Frontiers of Research and Technology (QFort), Tainan 70101, Taiwan. 11Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan. 12MU Materials Science & Engineering Institute, University of Missouri, Columbia, MO 65211, USA. 13These authors e-mail: ; ; ; contributed equally: Qiangsheng Lu, P. V. Sreenivasa Reddy, Hoyeon Jeon. Nature Communications | (2024)15:6001 1 Article https://doi.org/10.1038/s41467-024-50329-6 Fig. 1 | Topology, lattice property, and band structure of 2D Weyl semimetal, αbismuthene grown on SnS. a Overview of Dirac/Weyl semimetals and their topological boundary states. b Side and top views of the lattice structure of bismuthene and SnS substrate. The red dashed squares indicate the unit cell of bismuthene and SnS. c Large-scale STM image of bismuthene grown on SnS substrate. d The height profile is taken along the red arrow in (c). e Zoom-in STM images of bismuthene (top) and the surface of SnS (bottom). The red dashed squares indicate the unit cell of SnS and bismuthene. f Calculated band structure of free-standing bismuthene. g Calculated band structure of bismuthene on SnSe. existence of topologically protected edge states27. These topological edge states take the form of Fermi strings with one end attached to the projection of bulk Weyl nodes at the Fermi level, as schematically shown in Fig. 1a28. The Fermi string edge states serve as the 1D counterparts to the Fermi arc surface states observed in 3D Weyl semimetals. In this context, 2D Weyl semimetals present an unprecedented paradigm of bulk–boundary correspondence in topological materials. The highly unusual properties associated with 2D Weyl fermion states have inspired a myriad of theoretical and experimental works20,28–37. Nevertheless, the realization of an intrinsic 2D Weyl semimetal in experiments remains elusive to date. In this work, we report the realization of a 2D Weyl semimetal in an intrinsic 2D crystal, epitaxial bismuthene (a single atomic layer of bismuth stabilized in phosphorene structure38,39). Our spin- and angleresolved photoemission spectroscopy (spin-ARPES) results unambiguously demonstrate the spin-polarized Weyl fermion states in bismuthene grown on SnS(Se) substrates. Furthermore, our scanning tunneling spectroscopy (STS) measurements unveil a robustly Nature Communications | (2024)15:6001 2 Article enhanced local density of states at the edge of bismuthene, which aligns seamlessly with the calculated edge spectrum featuring Fermi string states. These experimental results establish epitaxial bismuthene on SnS(Se) as an ideal 2D Weyl semimetal. Results and discussion The material base for hosting 2D Weyl fermion states Each Bismuth atom typically forms three covalent bonds with its neighbors. Two allotropic structural phases of bismuthene exist in the 2D limit, namely, the orthorhombic phosphorene-like phase40,41 and the hexagonal honeycomb-like phase42,43. Here we grow the phosphorene-like bismuthene (bismuthene for short in the following) by molecular beam epitaxy (MBE). We selected SnS(Se) as the substrate due to its van der Waals semiconductor properties, and t (...truncated)