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 ͑dHvA͒ and the Shubnikov-de Haas ͑SdH͒ effects in a two-dimensional electron system ͑2DES͒ in a modulation-doped GaAs/ Al x Ga 1−x 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 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 ϫ 10 10 to 33ϫ 10 10 cm −2 . The wave forms of the dHvA oscillations were nonsinusoidal down to a magnetic field as small as 1.45 T. At the same time the zero-field mobility was as low as e =10 5 cm 2 / V s. We found that at fixed B the observed dHvA wave form and amplitude were independent of n s and 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.

Magnetometry of low-dimensional electron and hole systems

“…In Zhu's case the illumination reduced the disorder experienced by the extended states (which are the only ones influencing the transport mobility) while increasing that experienced by the localized states (to which dHvA measurements are also sensitive). The results of Ruhe et al [18] also point to the non-equivalence of these lifetimes, but further show that the differences can be quite extreme: by varying sample density with a gate and measuring transport and dHvA in the same sample they showed that the dHvA amplitude can be almost unaffected even as µ H is varied from 10 to 50 m 2 V −1 s −1 . However, they assert that the quantum lifetime in dHvA should "not be interpreted as a scattering time of electrons at the Fermi energy as is done in the case of SdH" but that it is a "measure for the broadening of the Landau levels and considers all occupied levels".…”

“…(Zawadzki [55] followed essentially this procedure in an early model of 2D dHvA, but assumed a delta function DOS.) The general procedure used for fixed N is thus as follows: (i) calculate µ from (19), using an iterative method such as bisection [51]; (ii) find Ω and hence F using (18) and (20); (iii) differentiate F with respect to B to find m (13). Alternatively, it is possible to replace steps (ii) and (iii) by differentiating Ω numerically at constant µ, but this requires twice the number of evaluations as the first method.…”

Magnetometry on quantum Hall systems: Thermodynamic energy gaps and the density of states distribution

“…Details are given in Refs. [18,27]. The advantage of this setup in addition to an enhanced sensitivity of up to…”

Frequency anomaly in the Rashba-effect induced magnetization oscillations of a high-mobility two-dimensional electron system

“…Thermodynamic quantities like the magnetization M are in particular powerful to study electronic states since they allow for an explicitly quantitative analysis and provide fundamental insight without further assumptions. 5,6 Bychkov and Rashba have addressed M of a 2DES with R-SOI in a pioneering theoretical work in 1984. 7 At zero temperature T the oscillatory behavior of M = −∂U/∂B| n s ,T =0 , that is, the de Haas-van Alphen (dHvA) effect, provides direct access to the evolution of the ground state energy U with B. n s is the carrier density.…”