Valley interference and spin exchange at the atomic scale in silicon

PBr3 adsorption on a chlorinated Si(100) surface with mono- and bivacancies

For the most precise incorporation of single impurities in silicon, which is utilized to create quantum devices, a monolayer of adatoms on the Si(100) surface and a dopant-containing molecule are used. Here, we studied the interaction of phosphorus tribromide with a chlorine monolayer with mono- and bivacancies using a scanning tunneling microscope (STM) at 77 K. The combination of different halogens in the molecule and the adsorbate layer enabled unambiguous identification of the structures after PBr3 dissociation on Si(100)-Cl. A Cl monolayer was exposed to PBr3 in the STM chamber, which allows us to compare the same surface areas before and after PBr3 adsorption. As a result of this comparison, we detected small changes in the chlorine layer and unraveled the molecular fragments filling mono- and bivacancies. Using density functional theory, we found that the phosphorus atom occupies a bridge position after dissociation of the PBr3 molecule, which primarily bonds with silicon in Cl bivacancies. These findings provide insight into the interaction of a dopant-containing molecule with an adsorbate monolayer on Si(100) and can be applied to improve the process of single impurity incorporation into silicon.

Atomic Engineering of Molecular Qubits for High-Speed, High-Fidelity Single Qubit Gates

Universal quantum computing requires fast single- and two-qubit gates with individual qubit addressability to minimize decoherence errors during processor operation. Electron spin qubits using individual phosphorus donor atoms in silicon have demonstrated long coherence times with high fidelities, providing an attractive platform for scalable quantum computing. While individual qubit addressability has been demonstrated by controlling the hyperfine interaction between the electron and nuclear wave function in a global magnetic field, the small hyperfine Stark coefficient of 0.34 MHz/MV m-1 achieved to date has limited the speed of single quantum gates to ∼42 μs to avoid rotating neighboring qubits due to power broadening from the antenna. The use of molecular 2P qubits with more than one donor atom has not only demonstrated fast (0.8 ns) two-qubit SWAP gates and long spin relaxation times of ∼30 s but provides an alternate way to achieve high selectivity of the qubit resonance frequency. Here, we show in two different devices that by placing the donors with comparable interatomic spacings (∼0.8 nm) but along different crystallographic axes, either the [110] or [310] orientations using STM lithography, we can engineer the hyperfine Stark shift from 1 MHz/MV m-1 to 11.2 MHz/MV m-1, respectively, a factor of 10 difference. NEMO atomistic calculations show that larger hyperfine Stark coefficients of up to ∼70 MHz/MV m-1 can be achieved within 2P molecules by placing the donors ≥5 nm apart. When combined with Gaussian pulse shaping, we show that fast single qubit gates with 2π rotation times of 10 ns and ∼99% fidelity single qubit operations are feasible without affecting neighboring qubits. By increasing the single qubit gate time to ∼550 ns, two orders of magnitude faster than previously measured, our simulations confirm that >99.99% single qubit control fidelities are achievable.

Influence of sample momentum space features on scanning tunnelling microscope measurements

Theoretical understanding of scanning tunnelling microscopy (STM) measurements involve electronic structure details of the STM tip and the sample being measured. Conventionally, the focus has been on the accuracy of the electronic state simulations of the sample, whereas the STM tip electronic state is typically approximated as a simple spherically symmetric s orbital. This widely used s orbital approximation has failed in recent STM studies where the measured STM images of subsurface impurity wave functions in silicon required a detailed description of the STM tip electronic state. In this work, we show that the failure of the s orbital approximation is due to the indirect band-gap of the sample material silicon (Si), which gives rise to complex valley interferences in the momentum space of impurity wave functions. Based on direct comparison of STM images computed from multi-million-atom electronic structure calculations of impurity wave functions in direct (GaAs) and indirect (Si) band-gap materials, our results establish that whilst the selection of STM tip orbital only plays a minor qualitative role for the direct band gap GaAs material, the STM measurements are dramatically modified by the momentum space features of the indirect band gap Si material, thereby requiring a quantitative representation of the STM tip orbital configuration. Our work provides new insights to understand future STM studies of semiconductor materials based on their momentum space features, which will be important for the design and implementation of emerging technologies in the areas of quantum computing, photonics, spintronics and valleytronics.