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

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 exceptional 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.