  Topological quantum phase transitions are characterised by changes in global
topological invariants. These invariants classify many body systems beyond the
conventional paradigm of local order parameters describing spontaneous symmetry
breaking. For non-interacting electrons, it is well understood that such
transitions are continuous and always accompanied by a gap-closing in the
energy spectrum, given that the symmetries protecting the topological phase are
maintained. Here, we demonstrate that sufficiently strong electron-electron
interaction can fundamentally change the situation: we discover a topological
quantum phase transition of first order character in the genuine thermodynamic
sense, that occurs without gap closing. Our theoretical study reveals the
existence of a quantum critical endpoint associated with an orbital instability
on the transition line between a 2D topological insulator and a trivial band
insulator. Remarkably, this phenomenon entails unambiguous signatures
associated to the orbital occupations that can be detected experimentally.
