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A systematic study of the energetics of electrons in an interface in amagnetic field is reported with exact analytical calculations based on a LandauLevel (LL) picture, by serious consideration of the finite thickness of theQuantum Well (QW). The approach is physically transparent and subtly differentin its line of reasoning from standard methods avoiding any semi-classicalapproximation. We find "internal" phase transitions (at partial LL filling) formagnetisation and susceptibility that are not captured by other approaches andthat give rise to nontrivial violations of the standard de Haas-van Alphenperiods, in a manner that reproduces the exact quantal astrophysical behavioursin the limit of full three-dimensional (3D) space. Upon inclusion of Zeemansplitting, additional features are also found, such as global energy minimaoriginating from the interplay of QW, Zeeman and LL Physics, while acorresponding calculation in a Composite Fermion picture with {\Lambda}-Levels,leads to new predictions on magnetic properties of an interacting electronliquid. By pursuing the same line of reasoning for a topologically nontrivialsystem with a relativistic spectrum, we find evidence that similar effectsmight be operative in the dimensionality crossover of 3D strong topologicalinsulators to 2D topological insulator quantum wells.

Thickness-induced violation of de Haas-van Alphen effect through exact analytical solutions at a one-electron and a one-Composite Fermion level