The fractional quantum Hall effect in a continuously variable density state-of-the-art 2DES

Johannes Nübler

Max-Plack-Institute for Solid State Research, Germany

J. Nübler(1), J. Smet(1), V. Umansky(2), M. Heiblum(2), K. v. Klitzing(1)
(1) Max-Planck-Institut für Festkörperforschung, Heisenbergstraße 1, D-70569 Stuttgart, Germany
(2) Braun Centre for Semiconductor Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
A main focus of today's research on two-dimensional electron systems (2DES) at low temperatures is the physics of fractional quantum Hall states. Due to its possible relevance for topological quantum computation [1], particular interest is attributed to the still mysterious even-denominator FQHE state at filling 5/2 that is conjectured to show fractional, non-abelian statistics [2]. A suitable tool to investigate the physics of these quantum phases is the continuous variation of parameters during measurement, as has been done in the literature ([3], [4], [5]). Here, we report on measurements of a state-of-the-art 2DES embedded in a 30 nm quantum well doped from one side using a new doping scheme [6]. The electron density can be varied continuously by a backgate by more that 100% up to above 2.5x10E11 /cm2. We correlate the quality of the 5/2 state with the electron mobility, the quantum lifetime and the resistivities of the composite fermion metallic states at filling 1/2 and 3/2.
Measurements at 10 mK show a linear dependence of the mobility on electron density, ranging from 6x10E6 cm2/Vs at low densities of 1.2x10E11 /cm2 up to 25x10E6 cm2/Vs at the highest densities. The quantum lifetime (extracted from low-field Shubnikov-de-Haas oscillations) is approximately constant in electron density and also exhibits strong temperature dependence. The resistivity of the composite fermion metallic states behaves non-linear as the density is tuned. These resistivities grow super-linear with decreasing density. Even at low densities of 1.2x10E11 /cm2 the longitudinal resistance shows a deep minimum at filling 5/2, accompanied by a plateau in the hall resistance. As the density is gradually increased, the plateau broadens and a finite region of vanishing longitudinal resistance develops. In parallel, quantized states emerge at fractional fillings 7/3, 8/3, 11/5 and 14/5 together with three reentrant integer quantum hall plateaus, all fully developed at the highest densities.
These findings open the way to detailed comparison with results from other continuous parameter variations like temperature and in-plane magnetic field in order to address still unresolved questions on the many nearly degenerate quantum phases in the first excited Landau level.
[1] S. Das Sarma, M. Freedman, C. Nayak, PRL 94 , 166802 (2005), Physics Today 59, 32 (2006).
[2] G. Moore, N. Read, Nucl. Phys. B 360, 362 (1991).
[3] C. R. Dean et al., arXiv: cond-mat/: 0801.3312; C. H. Choi et al., arXiv: cond-mat/: 0707.0236.
[4] G. A. Csáthy et al., PRL 94, 146801 (2005); W. Pan et al., PRL 83, 820 (1999).
[5] W. Pan et al., arXiv: cond-mat/: 0103144v2
[6] V. Umansky, M. Heiblum, Y. Levinson, J. Smet, J. Nübler, M. Dolev, to be published.