Spindle nodal chain in three-dimensional α' boron.

Topological metals/semimetals (TMs) have emerged as a new frontier in the field of quantum materials. A few two-dimensional (2D) boron sheets have been suggested as Dirac materials, however, to date TMs made of three-dimensional (3D) boron structures have not been found. Herein, by means of systematic first principles computations, we discovered that a rather stable 3D boron allotrope, namely 3D-α' boron, is a nodal-chain semimetal. In momentum space, six nodal lines and rings contact each other and form a novel spindle nodal chain. This 3D-α' boron can be formed by stacking 2D wiggle α' boron sheets, which are also nodal-ring semimetals. In addition, our chemical bond analysis revealed that the topological properties of the 3D and 2D boron structures are related to the π bonds between boron atoms, however, the bonding characteristics are different from those in the 2D and 3D carbon structures.