Topological states in the polymerized carbon nanotubes

Abstract

In this work, we report by ab initio calculations a systematical study on the energetic, dynamical, and electronic properties of polymerized (2n+1,0) (n=2,3,4) sing wall carbon nanotubes, termed as CNT(5,0), CNT(7,0), and CNT(9,0) carbon. The total energy calculations show that the equilibrium energies of the three carbon allotropes are lower than or comparable to the previously proposed bct-C16, bco-C16, and ors-C16 carbon. Their dynamical stabilities have been confirmed with phonon band spectrum calculations and their thermal stabilities have been confirmed with ab initio molecular dynamics simulations. Despite their unified space group symmetries and similar bonding types, their electronic properties are distinct: CNT(5,0) and CNT(7,0) carbon are topological nodal line semimetals with nodal rings in kx=0 and kz=0 mirror planes respectively, while the CNT(9,0) carbon is a semiconductor. To understand their distinct electronic behaviors, we provide a systematical explanation from the real space crystalline structure perspective. Our work has enriched the family of carbon allotropes with exotic band topologies and provide insights for the relations between real space crystalline structures and momentum space band topologies.