Controlling Hole Spin in Quantum Dots: Alloy Effects

Hole spins in semiconductor quantum dots (QD) are promising qubits. The Zeeman-split states form two-level systems with splitting determined by the physical spin of the state. Due to strong spin-orbit coupling, the hole spin orientation is locked to the QD axis for magnetic fields B away from the Voigt configuration. However, in Voigt configuration, the hole spin is nearly fully suppressed. Application of an electric field parallel or antiparallel to B in the Voigt configuration restores the hole spin and provides exquisite control of the spin orientation over a wide range of angles. This control is disrupted if the QD is an alloy. Tight-binding theory is used to describe InGaAs alloy quantum dots. The disorder of a random alloy configuration scrambles the hole distribution at the atomic scale. Applying a lateral electric field with B in Voigt configuration can restore the z component of the spin even with alloy disorder, but the in-plane spin remains small when the QD is disordered. We provide several examples to illustrate this alloy induced spin scrambling, show the dependence on alloy concentration, and discuss the effect on hole Zeeman splitting, g-factors, and the resulting spin control.