Fig. 1
From: Spin–orbit coupling in silicon for electrons bound to donors
Impact of the electromagnetic environment on a single P donor qubit in a nanoelectronic device. a Overview STM image of the readout device after hydrogen lithography, showing an SET charge sensor with source (S) and drain (D) electrodes, and four electrostatic gates (G1,2, GT and GSET). A 31P donor qubit was placed within the dashed white circle. Jagged lines horizontally across the image are atomic step edges on the Si(001)-2 × 1 surface. Inset: atomic-resolution close-up, showing the placement of the donor with respect to the SET island, as well as the orientation of the silicon dimer-rows parallel to [110]. b Alignment of the external magnetic field B (blue arrow) and dominant electric field Ey (green arrow), giving rise to an effective magnetic field Beff (red arrow). c Energy level diagram of a Si:P donor. d Measured spin-relaxation rates of bulk donors (black circles),28 rescaled to the low-temperature limit5 and B = 3.5 T, compared to valley repopulation (dashed black), single-valley (dashed light grey) theories, and their sum (solid black). e Spin-relaxation anisotropy measured for a single Si:P qubit in the nanoelectronic device of (a). The solid red line shows a fit to HEB theory. f Spin-relaxation rates 1/T1(B) along [001], [111] and [110], with a clear B5-dependence. Deviations at low-magnetic fields are likely due to dipole–dipole magnetic coupling with substrate dopants,3,5 or due to charge noise.31 Grey data points indicate spin readout using the D− charge state.4 Black arrows indicate B = 3.5 T used in our anisotropy measurements
