Abstract
In silicon spin qubits, the valley splitting must be tuned far away from the qubit Zeeman splitting to prevent fast qubit relaxation. In this work, we study in detail how the valley splitting depends on the electric and magnetic fields as well as the quantum dot geometry for both ideal and disordered Si/SiGe interfaces. We theoretically model a realistic electrostatically defined quantum dot and find the exact ground and excited states for the out-of-plane electron motion. This enables us to find the electron envelope function and its dependence on the electric and magnetic fields. For a quantum dot with an ideal interface, the slight cyclotron motion of electrons driven by an in-plane magnetic field slightly increases the valley splitting. Importantly, our modeling makes it possible to analyze the effect of arbitrary configurations of interface disorders. In agreement with previous studies, we show that interface steps can significantly reduce the valley splitting. Interestingly, depending on where the interface steps are located, the magnetic field can increase or further suppress the valley splitting. Moreover, the valley splitting can scale linearly or, in the presence of interface steps, non-linearly with the electric field.
Highlights
The spin of isolated electrons trapped in silicon-based heterostructures is very promising for building high performance and scalable qubits [1]
If the valley splitting becomes equal to the qubit Zeeman splitting, a condition known as spin-valley hotspot, the valley-spin mixing for the qubit excited state reaches its maximum and gives rise to a very fast qubit relaxation via electron-phonon interaction
While it has been speculated that the magnetic field can increase the valley splitting in the presence of interface steps [27,28], interestingly, we find that the magnetic field can both increase or further suppress the valley splitting depending on the locations of the steps
Summary
The spin of isolated electrons trapped in silicon-based heterostructures is very promising for building high performance and scalable qubits [1]. We model a realistic potential profile for a SiGe/Si/SiGe quantum dot by taking into account both Si/SiGe interfaces as well as an interface between SiGe and the insulating layer hosting the gate electrodes Within this model, we find the exact solution for the ground state as well as excited state envelope functions for the out-ofplane electron motion. In the presence of an in-plane magnetic field, a cyclotron motion of electrons takes place which tends to increase the electron probability amplitude at the Si/SiGe interface [24] This effect can, in turn, modify and increase the valley splitting. We denote the radius of the quantum dot along xby x0 and the radius along yby y0
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