Simultaneous measurement of the de Haas-van Alphen and the Shubnikov-de Haas effect in a two-dimensional electron system

In a simultaneous experiment we studied the de Haas–van Alphen (dHvA) and the Shubnikov–de Haas (SdH) effects in a two-dimensional electron system (2DES) in a modulation-doped GaAs∕AlxGa1−xAs heterostructure. For this, a gated 2DES mesa was monolithically integrated with a micromechnical cantilever with an interferometric fiber-optics readout. In situ measurement of the dHvA and SdH oscillations at 300mK in a magnetic field B allowed us to directly compare the variation of the ground state energy and the nonequilibrium transport behavior, respectively. This was done on a 2DES of a small carrier density ns ranging from 5×1010to33×1010cm−2. The wave forms of the dHvA oscillations were nonsinusoidal down to a magnetic field as small as 1.45T. At the same time the zero-field mobility was as low as μe=105cm2/Vs. We found that at fixed B the observed dHvA wave form and amplitude were independent of ns and μe. This was unexpected and in contrast to the established picture in the literature. To understand the dHvA effect quantitatively in a disordered 2DES our data suggest that energetic details of the disorder potentials have to be considered.