  Working in the category of smooth projective varieties over an algebraically
closed field of characteristic 0, we review notions of ampleness and numerical
nefness for Higgs bundles which "feel" the Higgs field and formulate criteria
of the Barton-Kleiman type for these notions. We give an application to minimal
surfaces of general type that saturate the Miyaoka-Yau inequality, showing that
their cotangent bundle is ample. This will use results by Langer that imply
that also for varieties over algebraically closed field of characteristic zero
the so-called Simpson system is stable.
