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 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 $\mathbf{k}\cdot \mathbf{p}$ 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.

arXiv comment17 pages, 5 figures

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Cited by in corpus (9)

• Two-body Wigner molecularization in asymmetric quantum dot spin qubits
• High-precision real-space simulation of electrostatically-confined few-electron states
• Theory of multi-dimensional quantum capacitance and its application to spin and charge discrimination in quantum-dot arrays
• Quantum estimation and remote charge sensing with a hole-spin qubit in silicon
• Envelope-function theory of inhomogeneous strain in semiconductor nanostructures
• Dressed basis sets for the modeling of exchange interactions in double quantum dots
• Giant Rabi frequencies between qubit and excited hole states in silicon quantum dots
• Anomalous zero-field splitting for hole spin qubits in Si and Ge quantum dots
• Inter- and intra-band Coulomb interactions between holes in silicon nanostructures