Relaxation of single-electron spin qubits in silicon in the presence of interface steps

Abstract

We develop a valley-dependent envelope function theory that can describe the effects of arbitrary configurations of interface steps and miscuts on the qubit relaxation time. For a given interface roughness, we show how our theory can be used to find the valley-dependent dipole matrix elements, the valley splitting, and the spin-valley coupling as a function of the electromagnetic fields in a Si/SiGe quantum dot spin qubit. We demonstrate that our theory can quantitatively reproduce and explain the result of experimental measurements for the spin relaxation time with only a minimal set of free parameters. Investigating the sample dependence of spin relaxation, we find that at certain conditions for a disordered quantum dot, the spin-valley coupling vanishes. This, in turn, completely blocks the valley-induced qubit decay. We show that the presence of interface steps can in general give rise to a strongly anisotropic behavior of the spin relaxation time. Remarkably, by properly tuning the gate-induced out-of-plane electric field, it is possible to turn the spin-valley hotspot into a "coldspot" at which the relaxation time is significantly prolonged and where the spin relaxation time is additionally first-order insensitive to the fluctuations of the magnetic field. This electrical tunability enables on-demand fast qubit reset and initialization that is critical for many quantum algorithms and error correction schemes. We therefore argue that the valley degree of freedom can be used as an advantage for Si spin qubits.

Theory of Silicon Spin Qubit Relaxation in a Synthetic Spin-Orbit Field

“…The quantity V v has been modeled in Ref. [17] as a function of the offset potential U 0 , the electric field F z and details of the periodic parts of the Bloch functions. We show the form of V v in Eq.…”

“…It has been discussed in detail in Ref. [17] how to find the valley-dependent envelope functions by solving Eq. ( 5); we review the solutions in Appendix B.…”

“…The term 2) is the Zeeman splitting caused by the homogeneous magnetic field, while H i−SOC in the same equation describes the intrinsic spin-orbit coupling in the silicon quantum well that is caused by the interface inversion asymmetry and contains Rashba and Dresselhaus-like terms. For a disordered quantum dot H i−SOC can be written as [17],…”

“…Moreover, the presence of interface steps breaks the inversion symmetry within the interface plane and therefore, it generally gives rise to a non-vanishing in-plane dipole matrix elements. A recently developed valley-dependent envelope function theory based on the effective mass approximation enables directly calculating the dipole matrix elements as well the spin-valley mixing caused by the intrinsic spin-orbit coupling [17]. The theory also implies that the interface roughness can lead to strong anisotropic spin-valley mixing and spin relaxation.…”

“…Here we build on the valley-dependent envelope function of Ref. [17] and study in detail the influence of a gradient magnetic field on the relaxation rate and the EDSR Rabi frequency of a single-electron Si/SiGe spin qubit for various configurations of interface steps. For certain positions for the interface steps, we show that our theory can qualitatively explain the experimental data in Ref.…”