  Measurements of current-voltage characteristics from ideal carbon nanotube
(CNT) field electron emitters of small apex radius have shown that these
emitters can exhibit a linear Fowler-Nordheim (FN) plot [e.g., Dean and
Chalamala, Appl. Phys. Lett., 76, 375, 2000]. From such a plot, a constant
(voltage-independent) characteristic field enhancement factor (FEF) can be
deduced. Over fifteen years later, this experimental result has not yet been
convincingly retrieved from first-principles electronic structure calculations,
or more generally from quantum mechanics (QM). On the contrary, several QM
calculations have deduced that the characteristic FEF should be a function of
the macroscopic field applied to the CNT. This apparent contradiction between
experiment and QM theory has been an unexplained feature of CNT emission
science, and has raised doubts about the ability of existing QM models to
satisfactorily describe experimental CNT emission behavior. In this work we
demonstrate, by means of a density functional theory analysis of single-walled
CNTs "floating" in an applied macroscopic field, the following significant
result. This is that agreement between experiment, classical-conductor CNT
models and QM calculations can be achieved if the latter are used to calculate
(from the "real" total-charge-density distributions initially obtained) the
distributions of $\textit{induced}$ charge-density, induced local fields and
induced local FEFs. The present work confirms, more reliably and in
significantly greater detail than in earlier work on a different system, that
this finding applies to the common "post-on-a-conducing plane" situation of CNT
field electron emission. This finding also brings out various further
theoretical questions that need to be explored.
