  Method of invariants is used to obtain effective kp-Hamiltonian with
position-dependent band parameters and correct boundary conditions for electron
and hole envelope functions in A3B5-heterostructures with arbitrary interface
orientation. It is shown that the presence of heterointerface yields additional
quadratic-in-k and linear-in-k terms in kinetic energy operator of electron and
hole due to non-commutativity of position-dependent band parameters and
momentum operator. In particular, the conduction band Hamiltonian is determined
by two position-dependent band parameters. Similarly for description of the
valence band kp-Hamiltonian the three Luttinger parameters are no longer
sufficient, and introducing of two additional parameters that determine
quadratic-in-k terms, and additional nonrelativistic linear-in-k term, is
necessary. The additional terms appear in kp-Hamiltonians due to interface
effective spin-orbit interaction and variation of the Bloch functions across
the interface. In the framework of this approach the two band hole
kp-Hamiltonian is derived. Presence of heterointerface gives rise to short
range interface corrections, which are determined by the method of invariants.
The new form of the Hamiltonian allows us to obtain the correct boundary
conditions for envelope functions of electron and hole in A3B5-heterostructures
with arbitrary orientated abrupt heterointerfaces.
