Spherical, cylindrical and tetrahedral symmetries; hydrogenic states at high magnetic field in Si:P

Phosphorous donors in silicon have an electronic structure that mimics the hydrogen atom, albeit on a larger length, smaller energy and smaller magnetic field scale. While the hydrogen atom is spherically symmetric, an applied magnetic field imposes cylindrical symmetry, and the solid-state analogue involves, in addition, the symmetry of the Si crystal. For one magnetic field direction, all six conduction-band valleys of Si:P become equivalent. New experimental data to high laboratory fields (30 T), supported by new calculations, demonstrate that this high symmetry field orientation allows the most direct comparison with free hydrogen.