Vanishing Zeeman energy in a two-dimensional hole gas

A clear signature of Zeeman split states crossing is observed in a Landau fan diagram of strained germanium two-dimensional hole gas. The underlying mechanisms are discussed based on a perturbative model yielding a closed formula for the critical magnetic fields. These fields depend strongly on the energy difference between the topmost and neighboring valence bands and are sensitive to the quantum well thickness, strain, and spin-orbit interaction. The latter is a necessary feature for the crossing to occur. This framework enables a straightforward quantification of the hole-state parameters from simple measurements, thus paving the way for its use in design and modeling of hole-based quantum devices.