Self-consistent electronic structure calculations in the envelope-function approximation are performed for InAs-GaSb superlattices, with a three-band $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}$ formalism and suitable boundary conditions. The subband dispersion for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ not parallel to the growth axis, realistically computed for the first time, obeys a no-crossing rule which opens small (\ensuremath{\lesssim}10 meV) gaps between conduction-band-like and valence-band-like subbands. It is therefore argued that the semimetallic behavior observed for periods $d\ensuremath{\ge}180$ \AA{} is dominated by extrinsic effects.
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