Electromechanical effects in carbon nanotubes: Ab initio and analytical tight-binding calculations

We perform ab initio calculations of charged graphene and single-wall carbon nanotubes (CNTs). A wealth of electromechanical behaviors is obtained. (1) Both nanotubes and graphene expand upon electron injection. (2) Upon hole injection, metallic nanotubes and graphene display a nonmonotonic behavior. Upon increasing hole densities, the lattice constant initially contracts, reaches a minimum, and then starts to expand. The hole densities at minimum lattice constants are 0.3 $|e|/\mathrm{atom}$ for graphene and between 0.1 and $0.3|e|/\mathrm{atom}$ for the metallic nanotubes studied. (3) Semiconducting CNT’s with small diameters $(d\lesssim 20\mathrm{\AA })$ always expand upon hole injection. (4) Semiconducting CNT’s with large diameters $\left(d\gtrsim 20\mathrm{\AA }\right)$ display a behavior intermediate between those of metallic and large-gap CNT’s. (5) The strain versus extra charge displays a linear plus power-law behavior, with characteristic exponents for graphene, metallic, and semiconducting CNT’s. All these features are physically understood within a simple tight-binding total-energy model.