InAs/GaSb interfaces; the problem of boundary conditions

We present here a derivation of phenomenological boundary conditions for envelope functions at the interface between an InAs layer and a GaSb layer. The overlap of the valence band of GaSb with the conduction band of InAs leads to a coupling between electrons with total angular momentum 1/2 and holes with total angular momentum 3/2. The method that we use to match these wave-functions is that of the minimizing of the total energy of the system including the surface energy. We consider the different spinor characters of the states explicitly, and derive the required boundary conditions, which are not dependent on any specific microscopic model. The proposed approach is general, and may be used to obtain boundary conditions for other complicated cases of interfaces.