Shallow acceptor levels in Si/Ge/Si quantum well heterostructures are characterized by resonant-tunneling spectroscopy in the presence of high magnetic fields. In a perpendicular magnetic field we observe a linear Zeeman splitting of the acceptor levels. In an in-plane field, on the other hand, the Zeeman splitting is strongly suppressed. This anisotropic Zeeman splitting is shown to be a consequence of the huge light-hole--heavy-hole splitting caused by a large biaxial strain and a strong quantum confinement in the Ge quantum well.
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