Tight-binding simulations of random alloy and strong spin-orbit effects in InAs/GaBiAs quantum dot molecules

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Self-assembled \ce{InAs} quantum dots (QDs), which have long hole-spin coherence times and are amenable to optical control schemes, have long been explored as building blocks for qubit architectures. One such design consists of vertically stacking two QDs to create a quantum dot molecule (QDM). The two dots can be resonantly tuned to form "molecule-like" coupled hole states with the hybridization of hole states otherwise localized in each respective dot. Furthermore, spin-mixing of the hybridized states in dots offset along their stacking direction enables qubit rotation to be driven optically, allowing for an all-optical qubit control scheme. Increasing the magnitude of this spin-mixing is important for optical quantum control protocols. We introduce the incorporation of dilute \ce{GaBi_xAs_{1-x}} alloys in the barrier region between the two dots, as \ce{GaBiAs} is expected to provide an increase in spin-mixing of the molecular states over \ce{GaAs}. Using an atomistic tight-binding model, we compute the properties of \ce{GaBi_xAs_{1-x}} and the modification of hole states that arise when the alloy is used in the barrier of an \ce{InAs} QDM. We show that an atomistic treatment is necessary to correctly capture non-traditional alloy effects of \ce{GaBiAs}. Additionally, an atomistic model allows for the study of configurational variances and clustering effects of the alloy. We find that in \ce{InAs} QDMs with a \ce{GaBiAs} inter-dot barrier, hole states are well confined to the dots up to an alloy concentration of 7%. By independently studying the alloy-induced strain and electronic scattering off \ce{Bi} and As orbitals, we conclude that an initial increase in QDM hole state energy at low Bi concentration is caused by the alloy-induced strain. Additionally, a comparison between the fully alloyed barrier and a partially alloyed barrier shows that fully alloying the barrier applies an asymmetric strain between the top and bottom dot. By lowering the energetic barrier between the two dots, \ce{GaBiAs} is able to promote the tunnel coupling of hole states in QDMs. We obtain a three fold increase of hole tunnel coupling strength in the presence of a 7% alloy. Additionally, we show how an asymmetric strain between the two dots caused by the alloy results in a shift in the field strength needed to bring the dots to resonance. We explore different geometries of QDMs to optimize the tunnel coupling enhancement the alloy can provide, as well as present evidence that the change in tunnel coupling may affect the heavy-hole and light-hole components of the ground state in a QDM. The strong spin-orbit coupling strength of \ce{GaBiAs} allows for the enhancement of spin-mixing in QDMs. A strong magnetic field can be applied directly in the TB Hamiltonian. In order to fit the TB results to a simple phenomenological Hamiltonian, we found it necessary to include second order magnetic field terms in the phenomenological Hamiltonian as a diamagnetic correction to the hole state energies. Fitting to the corrected phenomenological model, we obtain a three-fold enhancement for the spin-mixing strength of offset dots at 7% \ce{Bi}. Additionally, at higher alloy concentrations, a combination of enhanced spin-mixing and increase resonance change in g-factor results in intra-dot spin-mixing between Zeeman split states of the lower energy dot. A perturbative analysis of the magnetic field shows that both the spin-mixing and resonance g-factor change are effects of the Peierls contribution, or the component of the magnetic field applied to the effective spatial angular momentum of the wavefunction. When spin-orbit coupling is removed from the system, there is no longer a preferred alignment between the spin of the system and the Peierls effective angular momentum, thus removing any magnetic field effects of the Peierls contribution. The analysis of spin-orbit effects can be extended to single dots with in-plane magnetic and electric fields. This thesis concludes with some preliminary results utilizing electric fields, in conjunction with spin-locking effects provided by spin-orbit coupling, to manipulate the spin polarization in single dots. TB calculations with a magnetic field are performed to show the preferred alignment of the effective angular momentum, given by the geometry of the dot, also spatially locks the spin-polarization of hole states. An electric field can then be applied to bias the charge density to either side of the dot, using the spatial texture of the spin to obtain a spin polarized in $z$ while both the magnetic and electric field is in the $xy$-plane. The same perturbative analysis with the QDMs can be applied to show sufficient spin-orbit coupling is needed to generate such an effect. We propose the utilization of spin texture and electric fields as a novel method for rotating the spin in QDs.