L.W. Engel

Critical exponent in the fractional quantum Hall effect

Abstract We report the observation of a universal critical exponent in the fractional quantum Hall effect (FQHE) from a study of the temperature (T) dependent electron transport in between Landau level filling factors v = 2 5 and v = 1 3 , over a T range from 1.2 K to 22 mK. in an AlGaAs-GaAs heterostructure. Specifically, the maximum value of dp xy dB and the width of pxx show the same power law dependence on T, i.e. ~T−K. The critical exponent K=0.43 ± 0.02.This power law dependence is the same as that obtained in the integral quantum Hall effect (IQHE) [Wei et al., Phys. Rev. Lett. 61 (1988) 1294], in analogy to which our result indicates the existence of a divergent correlation length for the wavefunction of the quasi-particles in the FQHE for 1 3 2 5 . The localization to delocalization transition can be characterized by a universal critical exponent, k, in both the IQHE and the FQHE.

Observation of a giant dielectric constant in the re-entrant insulating phase of two-dimensional electrons

Abstract We have measured the radio frequency Reσxx and Imσxx of a high mobility two-dimensional electron system (2DES) and observed a giant dielectric constant (κxx > 1 × 104) in the reentrant insulating phase (RIP) around the 1 5 fractional quantum Hall liquid. Results from temperature and excitation-level studies provide new evidence for the Wigner crystal (WC) model of the RIP, where the WC is strongly pinned by residual impurities in close proximity to the 2DES.

Studies of the reentrant insulating phase around the 15 FQH liquid: I–V curves, noise, RF bias

We report on systematic studies of I–V and noise in the insulating phase around the 15 FQH liquid at B = 11.9 T. The noise and I–V data are correlated, and together they are consistent with a weakly pinned Wigner crystal for B below and immediately above the 15 FQH liquid. For B ⩾ 12.7 T, the system is in a more insulating regime, in which the noise vanishes, and which could be described as a Wigner glass. Preliminary results of a search for resonances or Shapiro steps in a 2DES are also presented.

Magnetotransport in a wide parabolic quantum well

Measurements of the magnetoresistance of a high-quality electron system realized in a selectively doped, parabolic AlxGa1−xAs well are reported. Quantum oscillations in the magnetoresistance are analyzed to obtain the electron densities of the electric subbands. These densities are in agreement with the predictions of a self-consistent calculation of the subband structure for this system. With the magnetic field B slightly tilted away from the sample plane, we observe a dramatic manifestation of the subband-Landau-level coupling. At low B, the magnetic depopulation of the hybrid (electric-magnetic) subbands occurs, while at higher fields, Shubnikov-de Haas-like oscillations (periodic in 1B) are observed as the Fermi level crosses the quantized energy levels associated with the lowest hybrid subband.

Inductive anomaly of two-dimensional electrons in the Wigner solid regime

Abstract We have investigated the small-signal frequency response of the GaAs AlGaAs two-dimensional electron system in the reentrant insulating phase around the ν = 1 5 fractional quantum Hall liquid from 0.2 to 2 MHz in the presence of a DC bias. When the sample is DC biased above the nonlinear conduction threshold, the insulating state exhibits an inductive AC response as the imaginary component of the conductivity (Im σxx) becomes negative. Moreover, Im σxx shows a broad minimum near a frequency which increases with increasing DC bias, in a manner consistent with the washboard oscillations of a magnetic-field-induced Wigner crystal.

Magnetotransport properties of double-layer systems in wide single quantum wells

Abstract We report magnetotransport measurements in coupled double-layer electron systems realized in wide quantum wells. In these systems the distance and the coupling between the layers can be changed continuously by varying the electron density in the well. When the coupling between the two electron layers is sufficiently weak, we observe the absence of quantum Hall states at odd filling factors. Our results are qualitatively consistent with a recent theoretical model proposed for the magnetic-field-driven destruction of the quatum Hall effect in double quantum wells.

Observation of finite-frequency scaling in the integer quantum hall effect

Abstract We present microwave measurements of the diagonal conductivity σ xx , in the integer quantum Hall regime. Our frequencies f were between 0.2 and 14 GHz, and the temperature T was ≳ 50 mK. Broadband Re(σ xx ), was measured by a transmission line method. The widths Δ B of Re(σ xx ) peaks between IQHE minima increase with f roughly as (Δ B ) α f 0.41 for f ≳ 1 GHz. At lower f the peak width dependence on f saturates. We interpret the increase in Δ B with f as due to dynamic scaling. The exponent, together with existing estimates of the localization length exponent v , yields a dynamic exponent z ≈ 1.

Fractional quantum Hall effect in multilayer electron systems

Abstract We present several novel quasi-two-dimensional electron systems with an additional degree of freedom. These include systems which contain two or more layers of electrons in close proximity so that interlayer Coulomb interactions are strong, and thick-layer electron systems in wide parabolic wells. The magneto-transport data in these systems exhibit new phenomena: examples include the observation of a fractional quantum Hall state at the even-denominator v= 1 2 filling and an insulating phase reentrant around the v=1/3 fractional state in a double-layer electron system in a wide quantum well.

I-V, Transport and Noise in the Insulating Phase Around the 1/5 FQH Liquid

We find two different kinds of I-V curves in the insulating phase around the 1/5 fractional quantum Hall liquid. Both show an increase in differential conductance for voltages ≲ lmV, and change with T in a gradual way. The present status of our experiments on I-V and noise is summarized.