  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 non-monotonic 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|/atom for graphene and between 0.1 and 0.3 |e|/atom for
the metallic nanotubes studied. (3)Semiconducting CNTs with small diameters (d
<~ 20 A) always expand upon hole injection; (4) Semiconducting CNTs with large
diameters (d >~ 20 A) display a behavior intermediate between those of metallic
and large-gap CNTs. (5) The strain versus extra charge displays a linear plus
power-law behavior, with characteristic exponents for graphene, metallic, and
semiconducting CNTs. All these features are physically understood within a
simple tight-binding total-energy model.
