  Topological insulators (TIs) are bulk insulators with exotic 'topologically
protected' surface conducting modes. It has recently been pointed out that when
stacked together, interactions between surface modes can induce diverse phases
including the TI, Dirac semimetal, and Weyl semimetal. However, currently a
full experimental understanding of the conditions under which topological modes
interact is lacking. Here, working with multilayers of the TI Sb$_2$Te$_3$ and
the band insulator GeTe, we provide experimental evidence of a multiple
topological modes in a single Sb$_2$Te$_3$-GeTe-Sb$_2$Te$_3$ structure.
Furthermore, we show that reducing the thickness of the GeTe layer induces a
phase transition from a Dirac-like phase to a gapped phase. By comparing
different multilayer structures we demonstrate that this transition occurs due
to the hybridisation of states associated with different TI films. Our results
demonstrate that the Sb$_2$Te$_3$-GeTe system offers strong potential towards
manipulating topological states as well as towards controlledly inducing
various topological phases.
