Particle-Hole Symmetry and the Fractional Quantum Hall Effect in the Lowest Landau Level.

We report on detailed experimental studies of a high-quality heterojunction insulated-gate field-effect transistor (HIGFET) to probe the particle-hole symmetry of the fractional quantum Hall effect (FQHE) states about half-filling in the lowest Landau level. The HIGFET is specially designed to vary the density of a two-dimensional electronic system under constant magnetic fields. We find in our constant magnetic field, variable density measurements that the sequence of FQHE states at filling factors ν=1/3,2/5,3/7… and its particle-hole conjugate states at filling factors 1-ν=2/3,3/5,4/7… have a very similar energy gap. Moreover, a reflection symmetry can be established in the magnetoconductivities between the ν and 1-ν states about half-filling. Our results demonstrate that the FQHE states in the lowest Landau level are manifestly particle-hole symmetric.

Enhancement of the ν = 5/2 fractional quantum Hall state in a small in-plane magnetic field.

Using a 50-nm-width ultraclean GaAs/AlGaAs quantum well, we have studied the Landau level filling factor ν=5/2 fractional quantum Hall effect in a perpendicular magnetic field B∼1.7 T and determined its dependence on tilted magnetic fields. Contrary to all previous results, the 5/2 resistance minimum and the Hall plateau are found to strengthen continuously under an increasing tilt angle 0<θ<25° (corresponding to an in-plane magnetic field 060°, and the composite fermion series [2+p/(2p±1), p=1,2] can be identified. Based on our results, we discuss the relevance of a Skyrmion spin texture at ν=5/2 associated with small Zeeman energy in wide quantum wells, as proposed by Wójs et al. [Phys. Rev. Lett. 104, 086801 (2010)].

Spin transition in the ν=8/3 fractional quantum Hall effect.

We present here the results from a density dependent study of the activation energy gaps of the fractional quantum Hall effect states at Landau level fillings ν=8/3 and 7/3 in a series of high quality quantum wells. In the density range from 0.5×10(11) to 3×10(11) cm(-2), the 7/3 energy gap increases monotonically with increasing density, supporting its ground state being spin polarized. For the 8/3 state, however, its energy gap first decreases with increasing density, almost vanishes at n~0.8×10(11) cm(-2), and then turns around and increases with increasing density, clearly demonstrating a spin transition.

Termination of two-dimensional metallic conduction near the metal-insulator transition in a Si/SiGe quantum well.

We report in this Letter our recent low-temperature transport results in a Si/SiGe quantum well with moderate peak mobility. An apparent metal-insulating transition is observed. Within a small range of densities near the transition, the conductivity σ displays a nonmonotonic temperature dependence. After an initial decrease at high temperatures, σ first increases with decreasing temperature T, showing a metallic behavior. As T continues decreasing, a downturn in σ is observed. This downturn shifts to a lower T at higher densities. More interestingly, the downturn temperature shows a power-law dependence on the mobility at the downturn position, suggesting that a similar downturn is also expected to occur deep in the apparent metallic regime at albeit experimentally inaccessible temperatures. This thus hints that the observed metallic phase in 2D systems might be a finite temperature effect.

Impact of disorder on the 5/2 fractional quantum Hall state.

We compare the energy gap of the ν = 5/2 fractional quantum Hall effect state obtained in conventional high mobility modulation-doped quantum-well samples with those obtained in high quality GaAs transistors (heterojunction insulated gate field-effect transistors). We are able to identify the different roles that long-range and short-range disorders play in the 5/2 state and observe that the long-range potential fluctuations are more detrimental to the strength of the 5/2 state than short-range potential disorder.

Pinning-mode resonance of a Skyrme crystal near Landau-level filling factor ν=1.

Microwave pinning-mode resonances found around integer quantum Hall effects, are a signature of crystallized quasiparticles or holes. Application of in-plane magnetic field to these crystals, increasing the Zeeman energy, has negligible effect on the resonances just below Landau-level filling ν=2, but increases the pinning frequencies near ν=1, particularly for smaller quasiparticle or hole densities. The charge dynamics near ν=1, characteristic of a crystal order, are affected by spin, in a manner consistent with a Skyrme crystal.

Observation of a pinning mode in a Wigner solid with ν=1/3 fractional quantum Hall excitations.

We report the observation of a resonance in the microwave spectra of the real diagonal conductivities of a two-dimensional electron system within a range of ∼ ± 0.015 from filling factor ν = 1/3. The resonance is remarkably similar to resonances previously observed near integer ν, and is interpreted as the collective pinning mode of a disorder-pinned Wigner solid phase of e/3-charged carriers.

Observation of reentrant phases induced by short-range disorder in the lowest Landau level of Al{x}Ga{1-x}As/Al{0.32}Ga{0.68}as heterostructures.

We report the observation of a reentrant quantum Hall effect in the lowest Landau level between filling factors of 2/3 and 3/5 in a Al{x}Ga{1-x}As/Al{0.32}Ga{0.68}As heterostructure sample with x=0.85%. A reentrant insulating phase is also observed between filling factors of 2/5 and 1/3, demonstrating particle-hole symmetry between these phases. A sample with x=0.21% shows much weaker reentrant features, indicating that increased short-range scattering, due to the Al alloy in the conduction channel, aids in the formation of these phases.

Scaling in plateau-to-plateau transition: a direct connection of quantum hall systems with the Anderson localization model.

The quantum Hall-plateau transition was studied at temperatures down to 1 mK in a random alloy disordered high mobility two-dimensional electron gas. A perfect power-law scaling with kappa=0.42 was observed from 1.2 K down to 12 mK. This perfect scaling terminates sharply at a saturation temperature of Ts approximately 10 mK. The saturation is identified as a finite-size effect when the quantum phase coherence length (Lphi proportional, T(-p/2)) reaches the sample size (W) of millimeter scale. From a size dependent study, Ts proportional, W(-1) was observed and p=2 was obtained. The exponent of the localization length, determined directly from the measured kappa and p, is nu=2.38, and the dynamic critical exponent z=1.

Pinning mode resonances of 2D electron stripe phases: effect of an in-plane magnetic field.

We study the anisotropic pinning-mode resonances in the rf conductivity spectra of the stripe phase of 2D electron systems around a Landau level filling of 9/2, in the presence of an in-plane magnetic field B(ip). The polarization along which the resonance is observed switches as B(ip) is applied, consistent with the reorientation of the stripes. The resonance frequency, a measure of the pinning interaction between the 2D electron systems and disorder, increases with B(ip). The magnitude of this increase indicates that disorder interaction is playing an important role in determining the stripe orientation.

Observation of pinning mode of stripe phases of 2D systems in high Landau levels.

We study the radio-frequency diagonal conductivities of the anisotropic stripe phases of higher Landau levels near half-integer fillings. In the hard direction, in which larger dc resistivity occurs, the spectrum exhibits a striking resonance, while in the orthogonal, easy direction, no resonance is discernible. The resonance is interpreted as a pinning mode of the stripe phase.

Anisotropic modification of the effective hole g factor by electrostatic confinement.

We investigate effects of lateral confinement on spin splitting of energy levels in 2D hole gases grown on [311] GaAs. We found that lateral confinement enhances anisotropy of spin splitting relative to the 2D gas for both confining directions. Unexpectedly, the effective g factor does not depend on the 1D energy level number N for B parallel[01[over ]1] while it has strong N dependence for B parallel[2[over ]33]. Apart from quantitative difference in the spin splitting of energy levels for the two orthogonal confinement directions, we also report qualitative differences in the appearance of spin-split plateaus, with nonquantized plateaus observed only for the confinement in the [01[over ]1] direction. In our samples we can clearly associate the difference with anisotropy of spin-orbit interactions.

Observation of a fractional quantum hall state at nu = 1/4 in a wide GaAs quantum well.

We report the observation of an even-denominator fractional quantum Hall state at nu = 1/4 in a high quality, wide GaAs quantum well. The sample has a quantum well width of 50 nm and an electron density of n(e) = 2.55 x 10(11) cm(-2). We have performed transport measurements at T - 35 mK in magnetic fields up to 45 T. When the sample is perpendicular to the applied magnetic field, the diagonal resistance displays a kink at nu = 1/4. Upon tilting the sample to an angle of theta = 20.3 degrees a clear fractional quantum Hall state emerges at nu = 1/4 with a plateau in the Hall resistance and a strong minimum in the diagonal resistance.

Pinning modes and interlayer correlation in high-magnetic-field bilayer Wigner solids.

We report studies of pinning mode resonances in the low total Landau filling (nu) Wigner solid of a series of bilayer hole samples with negligible interlayer tunneling and with varying interlayer separation d. Comparison of states with equal layer densities (p,p) to single layer states (p,0) produced in situ by biasing, indicates that there is interlayer quantum correlation in the solid at small d. Also, the resonance frequency at small d is decreased just near nu = 1/2 and 2/3, indicating the importance in the solid of correlations related to those in the fractional quantum Hall effects.

Disappearance of metal-like behavior in GaAs two-dimensional holes below 30 mK.

The zero-field temperature dependence of the resistivity of two-dimensional holes is observed to exhibit two qualitatively different characteristics for a fixed carrier density for which only the metallic behavior of the so-called metal-insulator transition is anticipated. As T is lowered from 150 to 0.5 mK, the sign of the derivative of the resistivity with respect to T changes from being positive to negative when the temperature is lowered below approximately 30 mK and the resistivity continuously rises with cooling down to 0.5 mK, suggesting a crossover from being metal-like to insulatorlike.

Astability and negative differential resistance of the Wigner solid.

We report spontaneous narrow band oscillations in the high field Wigner solid. These oscillations are similar to the recently seen and yet unexplained oscillations in the reentrant integer quantum Hall states. The current-voltage characteristic has a region of negative differential resistance in the current biased setup and it is hysteretic in the voltage biased setup. As a consequence of the unusual breakdown, the oscillations in the Wigner solid are of the relaxation type.

Intervalley gap anomaly of two-dimensional electrons in silicon.

We report here a systematic study of the energy gaps at the odd-integer quantum Hall states nu = 3 and 5 under tilted magnetic (B) fields in a high quality Si two-dimensional electron system. Out of the coincidence region, the valley splitting is independent of the in-plane fields. However, the nu = 3 valley gap differs by about a factor of 3 (Deltav approximately 0.4 vs 1.2 K) on different sides of the coincidence. More surprisingly, instead of reducing to zero, the energy gaps at nu = 3 and 5 rise rapidly when approaching the coincidence angles. We believe that such an anomaly is related to strong couplings of the nearly degenerate Landau levels.

Evidence for skyrmion crystallization from NMR relaxation experiments.

A resistively detected NMR technique was used to probe the two-dimensional electron gas in a GaAs/AlGaAs quantum well. The spin-lattice relaxation rate (1/T(1)) was extracted at near complete filling of the first Landau level by electrons. The nuclear spin of (75)As is found to relax much more efficiently with T --> 0 and when a well developed quantum Hall state with R(xx) approximately 0 occurs. The data show a remarkable correlation between the nuclear spin relaxation and localization. This suggests that the magnetic ground state near complete filling of the first Landau level may contain a lattice of topological spin texture, i.e., a Skyrmion crystal.

Scaling and universality of integer quantum Hall plateau-to-plateau transitions.

We have investigated the integer quantum Hall plateau-to-plateau transition in two-dimensional electrons confined to AlxGa(1-x)As-Al0.33Ga0.67As heterostructures over a broad range of Al concentration x. For x between 0.65% and 1.6%, where the dominant contribution to disorder is from the short-range alloy potential fluctuations, we observe a perfect power-law scaling in the temperature range from 30 mK to 1 K with a critical exponent kappa = 0.42 +/- 0.01.

Magnetic-field-induced insulating phases at large r s.

Exploring a two-dimensional hole system in the large r(s) regime we found a surprisingly rich phase diagram. At the highest densities, beside the nu =1/3, 2/3, and 2/5 fractional quantum Hall states, we observe both of the previously reported high field insulating and reentrant insulating phases. As the density is lowered, the reentrant insulating phase initially strengthens, then it unexpectedly starts weakening until it completely disappears. The intricate behavior of the insulating phases can be explained by a nonmonotonic melting line in the nu-r(s) phase space.