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M. Wolloch, G. Feldbauer, P. Mohn, J. Redinger, A. Vernes:
"Ab initio calculation of the real contact area on the atomic scale";
Physical Review B, 91 (2015), 19; 1954361 - 1954368.

We present an approach to determine the onset of contact between a tip and
a surface. The real contact area depending on the distance is calculated
using Bader's quantum theory of atoms in molecules. The jump to contact,
which is often observed in atomic force microscopy experiments, is used as
an indicator for the initial point of contact, which in turn is defined by
atomic relaxations and thus without the need of external parameters.
Within our approach the contact area is estimated by evaluating the zero
flux surfaces between the touching Bader atoms, where the necessary
electronic density cutoff for the Bader partitioning is calculated to
depend on the initial point of contact. Our proposed approach is therefore
completely ab initio and we are able to define and calculate the real area
of contact without imposing restrictions or free parameters. As a
prototype system we choose a tip made of a ten-atom tungsten pyramid above
a moiré layer of graphene on an fcc iridium (111) substrate. We find that
the contact area depends exponentially on the effective distance between
the tip apex and the surface atom directly below within the atomically
relaxed nanosystem.