Linear Hyperfine Tuning of Donor Spins in Silicon Using Hydrostatic Strain

Abstract

We experimentally study the coupling of group V donor spins in silicon to mechanical strain, and measure strain-induced frequency shifts that are linear in strain, in contrast to the quadratic dependence predicted by the valley repopulation model (VRM), and therefore orders of magnitude greater than that predicted by the VRM for small strains |ϵ|<10^{-5}. Through both tight-binding and first principles calculations we find that these shifts arise from a linear tuning of the donor hyperfine interaction term by the hydrostatic component of strain and achieve semiquantitative agreement with the experimental values. Our results provide a framework for making quantitative predictions of donor spins in silicon nanostructures, such as those being used to develop silicon-based quantum processors and memories. The strong spin-strain coupling we measure (up to 150 GHz per strain, for Bi donors in Si) offers a method for donor spin tuning-shifting Bi donor electron spins by over a linewidth with a hydrostatic strain of order 10^{-6}-as well as opportunities for coupling to mechanical resonators.

Radii of Rydberg states of isolated silicon donors

“…The calculations were done with the sp 3 d 5 s * model [44], in supercells with side L = 48a = 26 nm. On-site corrections were included on the impurity atom [45]. We can see thatρ at the end of the previous section), and this confirms that it may be neglected for the purpose of studying the excited states.…”

Pulsed electron spin resonance spectroscopy in the Purcell regime

“…22. In our devices, bismuth donor spins experience large strain when cooled to low temperature because of the differential thermal expansion of Al and Si 18,23 , which leads to ESR lines much broader than both κ and the Rabi frequency 2gα in our experiments. We model this by a constant distribution ρ δ .…”

Strain-Induced Spin-Resonance Shifts in Silicon Devices

“…Applying strain to a valley shifts its energy relative to the conduction band minimum, resulting in a rearrangement of the relative populations of each valley which can be described as a mixing of the donor A 1 and E states. The degree of mixing can be calculated using the "valley repopulation" model (VRM) [47], which predicts a quadratic shift of the hyperfine interaction with an applied strain [48]: The second-order model predicts shifts an order of magnitude larger than the VRM does, as well as displays bipolar frequencies due to its strong linear dependence.…”

“…Very recently, it was found that the hyperfine interaction of donors in silicon is also sensitive to the hydrostatic component of strain [48]. This result is surprising, as the VRM predicts no hyperfine reduction for strains that shift all of the valleys by the same energy.…”