Exchange coupling between silicon donors : The crucial role of the central cell and mass anisotropy
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Donors in silicon are now demonstrated as one of the leading candidates for implementing qubits and quantum information processing. Single qubit operations, measurements, and long coherence times are firmly established, but progress on controlling two qubit interactions has been slower. One reason for this is that the interdonor exchange coupling has been predicted to oscillate with separation, making it hard to estimate in device designs. We present a multivalley effective mass theory of a donor pair in silicon, including both a central cell potential and the effective mass anisotropy intrinsic in the Si conduction band. We are able to accurately describe the single donor properties of valley-orbit coupling and the spatial extent of donor wave functions, highlighting the importance of fitting measured values of hyperfine coupling and the orbital energy of the 1s levels. Ours is a simple framework that can be applied flexibly to a range of experimental scenarios, but it is nonetheless able to provide fast and reliable predictions. We use it to estimate the exchange coupling between two donor electrons and we find a smoothing of its expected oscillations, and predict a monotonic dependence on separation if two donors are spaced precisely along the  direction.
Pica , G , Lovett , B W , Bhatt , R N & Lyon , S A 2014 , ' Exchange coupling between silicon donors : The crucial role of the central cell and mass anisotropy ' Physical Review. B, Condensed matter and materials physics , vol 89 , no. 23 , 235306 . DOI: 10.1103/PhysRevB.89.235306
Physical Review. B, Condensed matter and materials physics
© 2014. American Physical Society.
This research was funded by the joint EPSRC (EP/I035536)–NSF (Grant No. DMR-1107606) Materials World Network grant (B.W.L., G.P., S.A.L.), partly by NSF MRSEC Grant No. DMR-0819860 (S.A.L.), and Department of Energy, Office of Basic Energy Sciences Grant No. DE-SC0002140 (R.N.B.). B.W.L. thanks the Royal Society for a University Research Fellowship and R.N.B. thanks the Institute for Advanced Study, Princeton, for hospitality during the period this work was written.
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