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For 2D topological insulators with strong electron-hole hybridization, suchas HgTe/CdTe quantum wells, the widely used 4 x 4 k.p Hamiltonian based on thefirst electron and heavy hole sub-bands yields an equal number of physical andspurious solutions, for both the bulk states and the edge states. For symmetricbands and zero wave vector parallel to the sample edge, the mid-gap bulksolutions are identical to the edge solutions. In all cases, the physical edgesolution is exponentially localized to the boundary and has been shownpreviously to satisfy standard boundary conditions for the wave function andits derivative, even in the limit of an infinite wall potential. The sametreatment is now extended to the case of narrow sample widths, where for eachspin direction, a gap appears in the edge state dispersions. For widths greaterthan 200 nm, this gap is less than half of the value reported for open boundaryconditions, which are called into question because they include a spurious wavefunction component. The gap in the edge state dispersions is also calculatedfor weakly hybridized quantum wells such as InAs/GaSb/AlSb. In contrast to thestrongly hybridized case, the edge states at the zone center only have pureexponential character when the bands are symmetric and when the sample hascertain characteristic width values.

A k.p treatment of edge states in narrow 2D topological insulators, with standard boundary conditions for the wave function and its derivative