Two-dimensional (2D) Dirac-like electron gases have attracted tremendous research interest ever since the discovery of free-standing graphene. The linear energy dispersion and nontrivial Berry phase play a pivotal role in the electronic, optical, mechanical, and chemical properties of 2D Dirac materials. The known 2D Dirac materials are gapless only within certain approximations, for example, in the absence of spin–orbit coupling (SOC). Here, we report a route to establishing robust Dirac cones in 2D materials with nonsymmorphic crystal lattice. The nonsymmorphic symmetry enforces Dirac-like band dispersions around certain high-symmetry momenta in the presence of SOC. Through μ-ARPES measurements, we observe Dirac-like band dispersions in α-bismuthene. The nonsymmorphic lattice symmetry is confirmed by μ-low-energy electron diffraction and scanning tunneling microscopy. Our first-principles simulations and theoretical topological analysis demonstrate the correspondence between nonsymmorphic symmetry and Dirac states. This mechanism can be straightforwardly generalized to other nonsymmorphic materials. The results enlighten the search of symmetry-enforced Dirac fermions in the vast uncharted world of nonsymmorphic 2D materials.
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Haldane topological spin-1 chains in a planar metal-organic framework
Haldane topological materials contain unique antiferromagnetic chains with symmetry-protected energy gaps. Such materials have potential applications in spintronics and future quantum computers. Haldane topological solids typically consist of spin-1 chains embedded in extended three-dimensional (3D) crystal structures. Here, we demonstrate that [Ni(μ−4,4′-bipyridine)(μ-oxalate)]n(NiBO) instead adopts a two-dimensional (2D) metal-organic framework (MOF) structure of Ni2+spin-1 chains weakly linked by 4,4′-bipyridine. NiBO exhibits Haldane topological properties with a gap between the singlet ground state and the triplet excited state. The latter is split by weak axial and rhombic anisotropies. Several experimental probes, including single-crystal X-ray diffraction, variable-temperature powder neutron diffraction (VT-PND), VT inelastic neutron scattering (VT-INS), DC susceptibility and specific heat measurements, high-field electron spin resonance, and unbiased quantum Monte Carlo simulations, provide a detailed, comprehensive characterization of NiBO. Vibrational (also known as phonon) properties of NiBO have been probed by INS and density-functional theory (DFT) calculations, indicating the absence of phonons near magnetic excitations in NiBO, suppressing spin-phonon coupling. The work here demonstrates that NiBO is indeed a rare 2D-MOF Haldane topological material.
more » « less- NSF-PAR ID:
- 10457849
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- Nature Communications
- Volume:
- 14
- Issue:
- 1
- ISSN:
- 2041-1723
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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