  Highly oriented pyrolytic graphite (HOPG) is an important substrate in many
technological applications and is routinely used as a standard in Scanning
Tunnelling Microscopy (STM) calibration, which makes the accurate
interpretation of the HOPG STM contrast of great fundamental and applicative
importance. We demonstrate by STM simulations based on electronic structure
obtained from first principles that the relative local orientation of the
STM-tip apex with respect to the HOPG substrate has a considerable effect on
the HOPG STM contrast. Importantly for experimental STM analysis of HOPG, the
simulations indicate that local tip-rotations maintaining a major contribution
of the $d_{3z^2-r^2}$ tip-apex state to the STM current affect only the
secondary features of the HOPG STM contrast resulting in "stripe" formation and
leaving the primary contrast unaltered. Conversely, tip-rotations leading to
enhanced contributions from $m\ne 0$ tip-apex electronic states can cause a
triangular-hexagonal change in the primary contrast. We also report a
comparison of two STM simulation models with experiments in terms of
bias-voltage-dependent STM topography brightness correlations, and discuss our
findings for the HOPG(0001) surface in combination with tungsten tip models of
different sharpnesses and terminations.
