Donor and Donor-Like EM Spectra

Radii of Rydberg states of isolated silicon donors

“…Using single-valley EMT works well for the excitedstate energies [14] (and our aim here is to assess the accuracy of the radius prediction for the excited states). We ignored an additional lattice-periodic factor [19,22,23] since it does not influence any of what follows or the intended application of engineering donor-donor interactions.…”

“…Effective mass theory (EMT) [14,[19][20][21][22][23] band minimum is far from k = 0 near the six equivalent X points of the Brillouin zone (along the 001 directions). These six valleys are anisotropic, characterized by a mass transverse to the valley axis m * t and a mass anisotropy parameter γ (= m * t /m * l where m * l is the mass along the axis).…”

“…The envelope functions f j,μ are solutions ofĤ μ f j,μ = ε j f j,μ . In the case that a magnetic field is applied parallel to the axis of the z valley, the Hamiltonian for that valley is [14,[33][34][35][36] …”

“…Qubit schemes being currently investigated that use excited states include a variety of species [6,12] including double donors such as selenium [13]. Amazingly, in spite of their ubiquity and enormous technical importance, measurement of the state radius of any isolated silicon impurity is lacking after more than six decades of research [14]. Regular arrays are desired for quantum computer architectures [7][8][9], for which information on the neighbor-neighbor interactions will be crucial, just as it is for free atoms [15].…”

“…Effective mass theory (EMT) [14,[19][20][21]23] may be used to predict the spectrum and the wave-function radius from three parameters; two effective mass values and the permittivity. We provide a self-consistent set of parameters obtained only from the zero-field spectrum and LZE, and use the resulting prediction for the QZE as an independent check on the validity of EMT.…”