Anticrossing and coupling of light-hole and heavy-hole states in (001) GaAs/AlxGa1-xAs heterostructures

Heterostructures sharing a common atom such as AlAs/GaAs/AlAs have a D-2d p oint-group symmetry which allows the bulk-forbidden coupling between odd-pa rity light-hole states (e.g., lh1) and even-parity heavy-hole states (e.g., hh2). Continuum models, such as the commonly implemented ("standard model" ) k.p theory miss the correct D-2d symmetry and thus produce zero coupling at the zone center. We have used the atomistic empirical pseudopotential th eory to study the lh1-hh2 coupling in (001) superlattices and quantum wells of GaAs/AlxGa1-xAs. By varying the Al concentration x of the barrier we sc an a range of valence-band barrier heights DeltaE(v)(x). We find the follow ing: (i) The lh1 and hh2 states anticross at rather large quantum wells wid th or superlattice periods 60 <n(c)< 70 monolayers. (ii) The coupling matri x elements V-lh1.hh2(k parallel to =0) are small (0.02-0.07 meV) and reach a maximum value at a valence-band barrier height DeltaE(v)approximate to 10 0 meV, which corresponds to an Al composition x(Al) = 0.2 in the barrier. ( iii) The coupling matrix elements obtained from our atomistic theory are at least an order of magnitude smaller than those calculated by the phenomeno logical model of Ivchenko et al. [Phys. Rev. B 54, 5852 (1996)]. (iv) The d ependence of V-lh1,V-hh2 on the barrier height DeltaE(v)(x) is more complic ated than that suggested by the recent model of Cortez et al., [J. Vac. Sci . Technol. B 18, 2232 (2000)], in which V-lh1.hh2 is proportional to the pr oduct of DeltaE(v)(x) times the amplitudes of the lh1 and hh2 envelopes at the interfaces. Thus, atomistic information is needed to establish the actu al scaling.