Interacting holes in Si and Ge double quantum dots: From a multiband approach to an effective-spin picture

The states of two electrons in tunnel-coupled semiconductor quantum dots can be effectively described in terms of a two-spin Hamiltonian with an isotropic Heisenberg interaction. A similar description needs to be generalized in the case of holes due to their multiband character and spin-orbit coupling, which mixes orbital and spin degrees of freedom and splits j = 3/2 and j = 1/2 multiplets. Here we investigate two-hole states in prototypical coupled Si and Ge quantum dots via different theoretical approaches. Multiband k . p and configuration-interaction calculations are combined with entanglement measures in order to thoroughly characterize the two-hole states in terms of band mixing and justify the introduction of an effective spin representation, which we analytically derive a from generalized Hubbard model. We find that, in the weak interdot regime, the ground state and first excited multiplet of the two-hole system display-unlike their electronic counterparts-a high degree of J mixing, even in the limit of purely heavy-hole states. The light-hole component additionally induces M mixing and a weak coupling between spinors characterized by different permutational symmetries.

Automated summary

In this study, two-hole states in prototypical coupled Si and Ge quantum dots were investigated using different theoretical approaches. It was found that, in the weak interdot regime, the ground state and first excited multiplet of the two-hole system displayed a high degree of mixing, even in the limit of purely heavy-hole states. The light-hole component further induced mixing and weak coupling between spinors characterized by different permutational symmetries.