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

Abstract

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 $\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ 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 $300\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$ 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 ${n}_{s}$ ranging from $5\ifmmode\times\else\texttimes\fi{}{10}^{10}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}33\ifmmode\times\else\texttimes\fi{}{10}^{10}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. The wave forms of the dHvA oscillations were nonsinusoidal down to a magnetic field as small as $1.45\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. At the same time the zero-field mobility was as low as ${\ensuremath{\mu}}_{e}={10}^{5}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}∕\mathrm{V}\phantom{\rule{0.2em}{0ex}}\mathrm{s}$. We found that at fixed $B$ the observed dHvA wave form and amplitude were independent of ${n}_{s}$ and ${\ensuremath{\mu}}_{e}$. 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.