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

Abstract

The states of two electrons in tunnel-coupled semiconductor quantum dots can be described in terms of a two-spin Hamiltonian with an isotropic Heisenberg interaction. A similar description does not apply in the case of holes due to their multiband character and spin-orbit coupling, which introduces a strong anisotropy in the angular-momentum space and mixes orbital and spin degrees of freedom. Here we investigate two-hole states in coupled Si and Ge quantum dots within a 6band k •p and Configuration-Interaction approach. We integrate and interpret the numerical results by means of an effective 4-band Hubbard model, which provides general expressions for the twohole eigenstates. The spin-orbit mixing in the single-and two-hole states is quantified via the computation of the linear entropy of the reduced spin density operator. We find that the ground state and first excited multiplet of the two-hole system are, respectively, a singlet and a triplet; however, differently from the one-band case, they are characterized by a combination of states belonging to different J subspaces, with dominant contributions coming respectively from even and odd values of J. Finally, by combining our numerical results with the effective model, we illustrate a pseudospin-1/2 description of the single-hole states which accounts for the main features of the lowest two-hole states in the regime of weak spin-orbit entanglement.