N c0n k0

Thus our nanostructure wavefunction will be written as nr) = E LA,B(7)unz0 (r)

and our objective will be to determine fA'B(r). The envelope function fA'B(r) depends of the kind of low-dimensional system.

2.5.1. Quasi-Two-Dimensional System

The quasi-two-dimensional systems are formed by multiple heterostructures such as quantum wells, multiple quantum wells, and superlattices. The envelope function in this case is fA'B{K, z) = -= exp(ik± ■ 7L)XA'B{z) (46)

where S is the sample area and k± = (kx' ky) is a two-dimensional wavevector which is the same in the A and B layers in order to preserve translational invariance in plane

Although k± could theoretically span the whole in-plane section of the host's Brillouin zone, it is in practice seldom larger than ~ 1/10 of its size.

We shall also assume that for all n, xA'B(z) varies slowly at the scale of the host's unit cell. Thus the heterostructure wavefunction ft(r) is a sum of the products of rapidly varying functions.

The heterostructure Hamiltonian can be written in the form

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