Theory of valley splitting and valley-induced relaxation of a single silicon spin qubit in the presence of interface disorder

In silicon spin qubits, the qubit must be tuned away from the spin-valley hotspot to prevent fast qubit relaxation. We study in detail how the valley splitting depends on the electric and magnetic fields for both ideal and disordered Si/SiGe interfaces. Importantly, our modeling makes it possible to analyze the effect of arbitrary configurations of interface steps. We find, depending on where the interface steps are located, the magnetic field can increase or suppress the valley splitting. Moreover, the valley splitting can scale linearly or, in the presence of interface steps, non-linearly with the electric field [1].

We then extend our analysis by developing a valley-dependent envelope function theory. One crucial set of parameters for understanding the behavior of spin relaxation is the inter-valley and intra-valley dipole matrix elements. Our analysis enables us to calculate the dipole matrix elements as a function of interface roughness, the in-plane orbital splitting, and the electromagnetic field. Interestingly, we find some specific highly disordered interfaces where the valley splitting is suppressed but remains finite whereas the inter-valley dipole matrix elements can vanish. In this case, we find that the spin-valley hotspot also disappears.

[1] arXiv: 2007.00332