  The two-dimensional topological insulating phase has been experimentally
discovered in HgTe quantum wells (QWs). The low-energy physics of
two-dimensional topological insulators (TIs) is described by the
Bernevig-Hughes-Zhang (BHZ) model, where the realization of a topological or a
normal insulating phase depends on the Dirac mass being negative or positive,
respectively. We solve the BHZ model for a mass domain configuration, analyzing
the effects on the edge modes of a finite Dirac mass in the normal insulating
region (soft-wall boundary condition). We show that at a boundary between a TI
and a normal insulator (NI), the Dirac point of the edge states appearing at
the interface strongly depends on the ratio between the Dirac masses in the two
regions. We also consider the case of multiple boundaries such as NI/TI/NI,
TI/NI/TI and NI/TI/NI/TI.

Mesoscale and Nanoscale Physics