Calculating the energy spectrum and electronic structure of two holes in a pair of strained Ge/Si coupled quantum dots

We theoretically investigate the energy spectrum and electronic structure of two vertically stacked Ge/Si quantum dots loaded with a pair of interacting holes, and study the dependence of basic physical characteristics on dot size and interdot separation. In particular, we focus on the splitting of the lowest spin singlet and triplet states and spatial correlations between holes. Here the term spin is rather an index for two Kramers degenerate states. The two holes are treated by six-band k center dot p calculations combined with the configuration-interaction model taking into account the realistic situation when both Si matrix and Ge nanoclusters are inhomogeneously strained. It is shown that asymmetry of strain distribution and spin-orbit coupling of the valence band introduce characteristic features in both single- and many-particle hole states, which are not captured by the usual one-band heavy-hole approximation. We find a level anticrossing between the lowest singlet and triplet states with a zero anticrossing energy gap as a function of interdot spacing. It is demonstrated that the level anticrossing between many-particle states is accompanied by a level crossing between single-particle bonding and antibonding molecular orbitals. We argue that both phenomena of level crossing and anticrossing originate from the asymmetry-induced localization of single-particle hole wave functions on different dots. Above a certain dot separation, the Mott-type delocalized-to-localized transition for the many-particle hole states is observed. We show that the transition is caused by the combined action of correlations and strain asymmetry.