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Degenerate conduction-band minima, or `valleys', in materials such as Si, AlAs, graphene, and MoS$_2$ allow them to host two-dimensional electron systems (2DESs) that can access a valley degree of freedom. These multivalley 2DESs present exciting opportunities for both pragmatic and fundamental research alike because not only are they a platform for valleytronic devices, but they also provide a tool to tune and investigate the properties of complex many-body ground states. Here, we report ultra-high quality, modulation doped AlAs quantum wells containing 2DESs that occupy two anisotropic valleys and have electron mobilities peaking at $2.4\times10^6$ cm$^{2}$V$^{-1}$s$^{-1}$ at a density of $2.2\times10^{11}$ cm$^{-2}$. This is more than an order of magnitude improvement in mobility over previous results. The unprecedented quality of our samples is demonstrated by magneto-transport data that show high-order fractional quantum Hall minima up to the Landau level filling $\nu=8/17$, and even the elusive $\nu=1/5$ quantum Hall state.

The fractional quantum Hall effect (FQHE) states at half integer Landau fillings ($\nu$) have long been of great interest, since they have correlations that differ from those of the fundamental Laughlin states found at odd denominators. At $\nu=1/2$ the FQHE has been observed in wide or double quantum wells, and is ascribed to the two-component Halperin-Laughlin $\Psi_{331}$ state. $\Psi_{331}$ excitations carry charge $\pm e/4$, like the carriers of $\nu=5/2$ states which are of interest in quantum computation. Further, such an excitation (quasiparticle or -hole) of $\Psi_{331}$ has unequal, opposite charge in the top and bottom layers, and hence an up or down dipole moment. Here we report evidence for a Wigner solid (WS) of such dipolar quasiholes from a quantitative study of the microwave spectra of a wide quantum well (WQW) at $\nu$ close to 1/2.

We have studied the temperature dependent resistivity at exactly half Landau level filling of a high-quality two-dimensional electron system in high magnetic field. The experimental data can be well described in terms of a standard degenerate system of fermions at zero magnetic field being scattered by impurities and acoustic phonons. The gauge-field-mediated phonon scattering contributes a ${T}^{\ensuremath{-}3}$ dependence to the composite fermion mobility. The effective mass of composite fermions is obtained from the temperature dependence of composite fermion-impurity scattering.

Today the fractional quantum Hall effect (FQHE) is well understood as the condensation of two-dimensional electrons in a high magnetic field into a sequence of quantum liquids. Thus far the relationship between the different liquids has been viewed as a hierarchy in which higher-order fractional states develop from the condensation of the elementary excitation of the next fewer-order fractional state. Recent theory has shed a new light on these relationships and provided us with a new framework for the FQHE. The central ingredients of this new picture are bizarre new particles, often termed composite fermions. This paper reviews our recent experimental evidence for the existence of such objects.

A new picture of fractional quantum Hall effect (FQHE) in terms of a novel particle called composite fermion has emerged recently. A composite fermion is a composite of two flux quanta which are effectively bound to an electron as a result of electron-electron interaction. A system of electrons at half-filled Landau level can be transformed to an equivalent system of composite fermions at zero effective magnetic field with a distinct Fermi surface. The FQHE is then viewed as the integral quantum Hall effect of composite fermions away ffrom half-filling. in order to test for these new particles, we have studied transport of anti-dot superlattices in a two-dimensional electron gas. At low magnetic fields electron transport exhibits well-known resonances at fields where the classical cyclotron orbit becomes commensurate with the anti-dot lattice. At half-filling we observe the same dimensional resonances. This establishes the “semi-classical” behavior of composite fermions.

Using single-electron capacitance spectroscopy, we map the magnetic field dependence of the ground state energies of a single quantum dot containing from 0 to 50 electrons. The experimental spectra reproduce many features of a noninteracting electron model with an added fixed charging energy. However, in detailed observations deviations are apparent: Exchange induces a two-electron singlet-triplet transition, self-consistency of the confinement potential causes the dot to assume a quasi-two-dimensional character, and features develop which are suggestive of the fractional quantum Hall effect.

We report on a strikingly linear behavior of the magnetoresistivity, ϱxx versus magnetic field B in two-dimensional electron systems at low-temperatures. While linearity of the Hall resistivity ϱxy versus magnetic field, punctuated in the region of the quantum Hall effect, is a direct consequence of the classical Hall geometry, there does not exist a theoretical basis for a linearity of ϱxx. The curious behavior of ϱxx is implicitly contained in a phenomenological relationship between ϱxx and ϱxy proposed earlier by Chang and Tsui. Our new data on very high mobility samples dramatically confirm their conjecture of this still unresolved proportionality between ϱxx and B dϱ xy dB .

We have studied edge magnetoplasmons (EMP's) created by pulses of 100 ps width in a high-mobility two-dimensional electron gas, using a cryogenic transistor. We find that magnetoplasmon motion along the edge occurs only in the direction expected for negatively charged electrons; there is no hint of propagation in the opposite direction expected for positively charged quasiholes. We also measure the periods and decay rates of the edge modes continuously as a function of the magnetic field. From these characteristics we deduce the width of the EMP boundary layer as well as the magnetic-field-dependent momentum-relaxation time.

We demonstrate that ballistic electrons in ultra-high mobility two-dimensional electron systems can be controlled in ways analogous to the manipulation of photons in optical systems. Among the electron-optical structures we demonstrate are emitters, detectors, absorbers, and refractors. These advances may enable the design of new types of electronic circuits.

Understanding the flow of spins in magnetic layered structures has enabled an increase in data storage density in hard drives over the past decade of more than two orders of magnitude1. Following this remarkable success, the field of 'spintronics' or spin-based electronics is moving beyond effects based on local spin polarisation and is turning its attention to spin-orbit interaction (SOI) effects, which hold promise for the production, detection and manipulation of spin currents, allowing coherent transmission of information within a device. While SOI-induced spin transport effects have been observed in two- and three-dimensional samples, these have been subtle and elusive, often detected only indirectly in electrical transport or else with more sophisticated techniques. Here we present the first observation of a predicted 'spin-orbit gap' in a one-dimensional sample, where counter-propagating spins, constituting a spin current, are accompanied by a clear signal in the easily-measured linear conductance of the system., Comment: 10 pages, 5 figures, supplementary information

We present a spectrum of experimental data on the fractional quantum Hall effect (FQHE) states in the first excited Landau level, obtained in an ultrahigh mobility two-dimensional electron system (2DES) and at very low temperatures and report the following results: For the even-denominator FQHE states, the sample dependence of the nu=5/2 state clearly shows that disorder plays an important role in determining the energy gap at nu=5/2. For the developing nu=19/8 FQHE state the temperature dependence of the Rxx minimum implies an energy gap of ~5mK.The energy gaps of the odd-denominator FQHE states at nu=7/3 and 8/3 also increase with decreasing disorder, similar to the gap at 5/2 state. Unexpectedly and contrary to earlier data on lower mobility samples, in this ultra-high quality specimen, the nu=13/5 state is missing, while its particle-hole conjugate state, the nu=12/5 state, is a fully developed FQHE state. We speculate that this disappearance might indicate a spin polarization of the nu=13/5 state. Finally, the temperature dependence is studied for the two-reentrant integer quantum Hall states around nu=5/2 and is found to show a very narrow temperature range for the transition from quantized to classical value., to be published

We have observed a rapid decrease in the rate by which two-dimensional electrons in very high-mobility (\ensuremath{\mu}\ensuremath{\approxeq}${10}^{7}$ ${\mathrm{cm}}^{2}$/V sec) GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As heterostructures are scattered by acoustic phonons as the temperature approaches T=0. This precipitous drop in scattering rate is caused by strong phase-space restrictions for electron-phonon scattering. The characteristic temperature for this transition is not the Debye temperature of the GaAs host material, but the temperature at which phonons of twice the Fermi wave vector cease to be thermally excited.

We have observed quantization of the diagonal resistance, R{sub xx}, at the edges of several quantum Hall states. Each quantized R{sub xx} value is close to the difference between the two adjacent Hall plateaus in the off-diagonal resistance, R{sub xy}. Peaks in R{sub xx} occur at different positions in positive and negative magnetic fields. Practically all R{sub xx} features can be explained quantitatively by a 1%/cm electron density gradient. Therefore, R{sub xx} is determined by Rxy and unrelated to the diagonal resistivity {rho}{sub xx}. Our findings throw an unexpected light on the empirical resistivity rule for 2D systems.

Magnetotransport measurements were performed in a ultra-high mobility GaAs/AlGaAs quantum well of density $\sim 3.0 \times 10^{11}$ $cm^{-2}$. The temperature dependence of the magnetoresistance $R_{xx}$ was studied in detail in the vicinity of $\nu={9/2}$. In particular, we discovered new minima in $R_{xx}$ at filling factor $\nu\simeq 4{1/5}$ and $4{4/5}$, but only at intermediate temperatures $80\lesssim T\lesssim 120$ mK. We interpret these as evidence for a fractional quantum Hall liquid forming in the N=2 Landau level and competing with bubble and Wigner crystal phases favored at lower temperatures. Our data suggest that a magnetically driven insulator-insulator quantum phase transition occurs between the bubble and Wigner crystal phases at T=0., Comment: Phys. Rev. Lett.93 266804 (2004)

We have resolved the bound states of a one-dimensional quantum wire by resonant electron tunneling. The atomically precise quantum-confined structure was prepared by cleaved-edge overgrowth in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As molecular-beam epitaxy. Tunneling proceeded, in a planar geometry, from the edge of a two-dimensional electron source through the bound states of the quantum wire into the edge of a two-dimensional electron drain. The experimental resonance positions, as well as their density dependences, are well reproduced by our self-consistent theoretical calculations.

We observe the capacitance signal resulting from single electrons tunneling into discrete quantum levels. The electrons tunnel between a metallic layer and confined states of a single disk in a microscopic capacitor fabricated in GaAs. Charge transfer occurs only for bias voltages at which a quantum level resonates with the Fermi energy of the metallic layer. This creates a sequence of distinct capacitance peaks whose bias positions directly reflect the electronic spectrum of the confined structure. From the magnetic field evolution of the spectrum, we deduce the nature of the bound states.

The FQHE has been studied in GaAs/AlGaAs heterostructures of mobility 5 × 106 cm2/V·s. Activation energies of the thirds states at v = 13, 23 far exceed earlier results, and comparison is made to theoretical values. These samples allowed observation of quantization in ϱXY at v=27 and v=15. Results from higher density samples display the hierarchical series up to v=613.

We report magnetotransport measurements on low-density, high-mobility two-dimensional (2D) electron systems in (Al,Ga)As/GaAs heterostructures down to Landau-level filling factors of $v\ensuremath{\sim}\frac{1}{18}$. We observe a striking activated temperature dependence with onset near $v\ensuremath{\sim}\frac{1}{5}$ and continuing to smallest $v$. The activation energy increase is approximately linear with decreasing $v$ and its slope depends monotonically on 2D density. While magnetic-field-induced localization cannot be ruled out, several features of the results are consistent with the formation of a pinned 2D Wigner crystal.

GeAu films operating near the metal insulator transition are ideally suited for high magnetic field thermometry. Until now, difficulties in fabrication, unpredictable temperature responsivity and their inherently high impedances(R up to 100M ohms) have prevented their uses as fast heat pulse detectors. It has been found [1] that within a narrow window of Au concentration that these films have excellent temperature responses. However, these concentrations were determined by Rutherford backscattering after fabrication. Variations on either side of this window resulted in films that are metallic(small R(T)) or insulating (exceedingly large resistances). In addition the responsivity was strongly dependent on whether or not these films were amorphous or polycrystalline.