Abstract
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 and multiplets. Here we investigate two-hole states in prototypical coupled Si and Ge quantum dots via different theoretical approaches. Multiband 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 mixing, even in the limit of purely heavy-hole states. The light-hole component additionally induces mixing and a weak coupling between spinors characterized by different permutational symmetries.
- Received 20 April 2021
- Revised 30 June 2021
- Accepted 30 June 2021
DOI:https://doi.org/10.1103/PhysRevB.104.035302
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