  We perform atomistic computer simulations to study the mechanism of
homogeneous dislocation nucleation in two dimensional (2D) hexagonal
crystalline films during indentation with a circular nanoindenter. The
nucleation process is governed by the vanishing of the energy associated with a
single normal mode. This critical mode is largely confined to a single plane of
adjacent atoms. For fixed film thickness, L, the spatial extent, \xi, of the
critical mode grows with indenter radius, R. For fixed R/L, the spatial extent
\xi, grows roughly as \xi ~ L^0.4. We, furthermore, perform a mesoscale
analysis to determine the lowest energy normal mode for mesoscale regions of
varying radius, r_{meso}, centered on the critical mode's core. The energy,
\lambda_{meso}, of the lowest normal mode in the meso-region decays very
rapidly with r_{meso} and \lambda_{meso} ~= 0 for r_{meso} >~ \xi. The lowest
normal mode shows a spatial extent, \xi_{meso}, which has a sublinear power-law
increase with r_{meso} for r_{meso} <~ \xi, and saturates at r_{meso} \gtrsim
1.5\xi. We demonstrate a universal relationship between \xi_{meso}/ \xi versus
r_{meso}/ \xi: independent of film thickness or indenter radius. The scenario
that emerges is one where the analysis of small regions, r_{meso} <~ \xi, in
the material \emph{can} reveal the presence of incipient instability even when
the region being probed is much smaller than the spatial extent of the critical
mode. However, the mesoscale analysis gives good estimates for the energy and
spatial extent of the critical mode \emph{only} for r_{meso} >~ 1.5 \xi. In
this sense homogeneous dislocation nucleation should be understood as a
quasi-local phenomenon.
