Three-dimensional honeycomb carbon: Junction line distortion and novel emergent fermions

Abstract Carbon enjoys a vast number of allotropic forms, each possessing unique properties determined by the lattice structures and bonding characters. Here, based on first-principles calculations, we propose a new three-dimensional carbon allotrope—hC28. We show that hC28 possesses excellent energetic, dynamical, thermal, and mechanical stability. It is energetically more stable than most other synthesized or proposed carbon allotropes. The material has a relatively small bulk modulus, but is thermally stable at temperatures as high as 2000 K. The structural, mechanical, X-ray diffraction, and electronic properties are systematically investigated. Particularly, we show that its low-energy band structure hosts multiple unconventional emergent fermions, including the quadratic-contact-point fermions, the birefringent Dirac fermions, and the triple-point fermions. We construct effective models to characterize each kind of fermions. Our work not only discovers a new carbon allotropic form, it also reveals remarkable mechanical and electronic properties for this new material, which may pave the way towards both fundamental studies as well as practical applications.