  The de Haas-van Alphen effect (dHvAe) describes the periodic oscillation of
the magnetisation in a material as a function of inverse applied magnetic
field. It forms the basis of a well established procedure for measuring Fermi
surface properties and its observation is typically taken as a direct signature
of a system being metallic. However, certain insulators can show similar
oscillations of the magnetisation from quantisation of the energies of electron
states in filled bands. Recently the theory of such an ${\it anomalous}$ dHvAe
(AdHvAe) has been worked out but so far there is no clear experimental
observation. Here, we show that the inverted narrow gap regime of InAs/GaSb
quantum wells is an ideal platform for the observation of the AdHvAe. From our
microscopic calculations we make quantitative predictions for the relevant
magnetic field and temperature regimes, and describe unambiguous experimental
signatures.
