

Theory
Hamiltonian
The Hamiltonian is derived from the group theory [2]. The k•p Hamiltonian is represented by an 8x8 matrix whose rows and columns are ordered according to the sequence of the basis function set:

(4) 
The matrix Hamiltonian with respect to the chosen basis can be written as

(5) 
consisting of the intraband matrices H_{cc}, H_{vv} and H_{ss} along the diagonal, that describe conduction band, heavy and light hole valence bands and splitoff valence band respectively, interband matrices H_{cv}, H_{cs}, H_{vs} and their Hermitianconjugative counterparts H_{vc}, H_{sc}, H_{sv}, that describe coupling between different bands. The H_{cc} matrix is

(6) 
where E_{g} is band gap, m_{0} is free electron mass, a_{c} is deformation potential of the conduction band, ε is a sum of diagonal elements of the strain tensor ε_{ij}, A' describes contribution to the eightband Hamiltonian from other band. The H_{vv} matrix is

(7) 
The first and the second terms are also known as LuttingerKohn 4x4 Hamiltonian [3] with strain according to the BirPikus description [4]:

(8) 
where

(9) 
and

(10) 
where

(11) 
Here a_{v}, b and d are valence band deformation potentials, γ_{1}, γ_{2} and γ_{3} are Luttingerlike parameters and connected to Luttinger parameters γ_{i} through [5]

(12) 
where P is momentum matrix element of the interaction between conduction and valence bands. The Kane P parameter is usually used in form of E_{p}, where

(13) 
The H^{vv}_{kl} and H^{vv}_{ek} terms describe klinear and εklinear coupling between light and heavy hole valence bands:

(14) 

(15) 
where

(16) 
The constant C weights the klinear terms in the valence bands. The H_{ss} matrix describing splitoff band is

(17) 
where Δ is the spinorbit splitoff energy. The H_{cv} and H_{cs} matrices are
where
and
Here B is ksquare coupling between conduction and valence bands, C_{2} is matrix element of simultaneous interaction of conduction and valence bands by the k•p and strain operator. The H_{vs} matrix consists of four terms:
The first and the second terms come from LuttingerKohn and BirPikus Hamiltonian:
where
and
where
The H^{vs}_{kl} and H^{vs}_{εk} terms describe klinear and εklinear coupling between valence and splitoff bands:
