  We propose a minimal effective two-dimensional Hamiltonian for HgTe/CdHgTe
quantum wells (QWs) describing the side maxima of the first valence subband. By
using the Hamiltonian, we explore the picture of helical edge states in tensile
and compressively strained HgTe QWs. We show that both dispersion and
probability density of the edge states can differ significantly from those
predicted by the Bernevig-Hughes-Zhang (BHZ) model. Our results pave the way
towards further theoretical investigations of HgTe-based quantum spin Hall
insulators with direct and indirect band gaps beyond the BHZ model.
