Exchange coupling between silicon donors: The crucial role of the central cell and mass anisotropy

Abstract

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 [100] direction.

Hyperfine Stark effect of shallow donors in silicon

“…Nonetheless, the Stark shift of Bi is still correctly found to be the lowest of the V group donors. We underline that any simpler MV EMT, including our previous work [40], could not get such consistent agreement across all donors, due to (21), as a function of the applied uniform field E, for all donors considered here. The field range shown is typical of those required for executing quantum gates and corresponds to the range investigated experimentally in Sec.…”

“…C 0 (k 0q , k 0q ) = 1, C 0 (k 0q , k 0−q ) = −0.1728 and C 0 (k 0q , k 0±p ) = 0.4081(p = q), as further detailed in Ref. 40, are due to the lattice-periodic portion of the Bloch functions involved:…”

“…While the variational method is expected to give reliable predictions of the binding energies, care must be taken when using it to probe the exact nature of the wave function: this is the reason why many different pseudopotentials and EMT approximations used in the past have led to satisfactory binding energies, but poor wave functions. As a first improvement, in a previous paper [40] we highlighted the importance of using anisotropic envelopes and imposing further constraints on the shape of the wave function, as indicated by experimental measurements. More precisely, we set the trial ground state function of a Si:P electron to match the experimental contact hyperfine coupling, which is proportional to the value of the electron density at the impurity site.…”

Surface code architecture for donors and dots in silicon with imprecise and nonuniform qubit couplings

“…This theoretical approach has been introduced in Refs. 35,36, and the details of how it has been adapted to the system considered here are given The adiabatic transfers take place thanks to the J coupling turned on at the crossing points of the Dot/ESR levels (∆ = 0), while 'phase erasing' steps allow the final quantum state to be independent of the evolution induced by each particular J. All operations require a few µs.…”

“…This feature is intrinsic to the silicon band structure 21,34,35 , and makes high-fidelity hard to attain with the dynamical phase gates proposed in donor-based quantum computers proposals 2 . In Fig.…”