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What are the ground states of an interacting, low-density electron system? In the absence of disorder, it has long been expected that as the electron density is lowered, the exchange energy gained by aligning the electron spins should exceed the enhancement in the kinetic (Fermi) energy, leading to a (Bloch) ferromagnetic transition. At even lower densities, another transition to a (Wigner) solid, an ordered array of electrons, should occur. Experimental access to these regimes, however, has been limited because of the absence of a material platform that supports an electron system with very high quality (low disorder) and low density simultaneously. Here we explore the ground states of interacting electrons in an exceptionally clean, two-dimensional electron system confined to a modulation-doped AlAs quantum well. The large electron effective mass in this system allows us to reach very large values of the interaction parameterrs, defined as the ratio of the Coulomb to Fermi energies. As we lower the electron density via gate bias, we find a sequence of phases, qualitatively consistent with the above scenario: a paramagnetic phase at large densities, a spontaneous transition to a ferromagnetic state whenrssurpasses 35, and then a phase with strongly nonlinear current-voltage characteristics, suggestive of a pinned Wigner solid, whenrsexceeds≃38. However, our sample makes a transition to an insulating state atrs≃27, preceding the onset of the spontaneous ferromagnetism, implying that besides interaction, the role of disorder must also be taken into account in understanding the different phases of a realistic dilute electron system.

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There has been a surge of recent interest in the role of anisotropy in interaction-induced phenomena in two-dimensional (2D) charged carrier systems. A fundamental question is how an anisotropy in the energy-band structure of the carriers at zero magnetic field affects the properties of the interacting particles at high fields, in particular of the composite fermions (CFs) and the fractional quantum Hall states (FQHSs). We demonstrate here tunable anisotropy for holes and hole-flux CFs confined to GaAs quantum wells, via applying in situ in-plane strain and measuring their Fermi wavevector anisotropy through commensurability oscillations. For strains on the order of 10 −4 we observe significant deformations of the shapes of the Fermi contours for both holes and CFs. The measured Fermi contour anisotropy for CFs at high magnetic field (αCF) is less than the anisotropy of their low-field hole (fermion) counterparts (αF), and closely follows the relation: αCF = √ αF.The energy gap measured for the ν = 2/3 FQHS, on the other hand, is nearly unaffected by the Fermi contour anisotropy up to αF ∼ 3.3, the highest anisotropy achieved in our experiments.High-mobility, two-dimensional (2D), charged carriers at high perpendicular magnetic fields B and low temperatures exhibit rich many-body physics driven by Coulomb interaction. Examples include the fractional quantum Hall state (FQHS), Wigner crystal, and stripe phase [1,2]. Recently, the role of anisotropy has become a focus of new studies . This interest has been amplified by the recognition that, although the FQHSs at fillings 1/q (q = odd integer) are well described by Laughlin's wave function with a rotational symmetry [24], there is a geometric degree of freedom associated with the anisotropy of the 2D carrier system [8].The fundamental issue we address here is how the anisotropy of the energy-band structure of the low-field carriers transfers to the interacting particles at high B and, in particular, to the FQHSs and composite fermions (CFs). The latter are electron-flux quasi-particles that form a Fermi sea at a half-filled Landau level [2,25], and provide a simple explanation for the nearby FQHSs [26].

Degenerate conduction-band minima, or 'valleys', in materials such as Si, AlAs, graphene, and MoS2 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 × 10 6 cm 2 V −1 s −1 at a density of 2.2 × 10 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 ν = 8/17, and even the elusive ν = 1/5 quantum Hall state.

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The two-dimensional electron system in an InAs quantum well has emerged as a prime candidate for hosting exotic quasi-particles with non-Abelian statistics such as Majorana fermions and parafermions. To attain its full promise, however, the electron system has to be clean enough to exhibit electron-electron interaction phenomena. Here we report the observation of fractional quantum Hall effect in a very low disorder InAs quantum well with a well-width of 24 nm, containing a two-dimensional electron system with a density $n=7.8 \times 10^{11}$ cm$^{-2}$ and low-temperature mobility $1.8 \times 10^6$ cm$^2$/Vs. At a temperature of $\simeq35$ mK and $B\simeq24$ T, we observe a deep minimum in the longitudinal resistance, accompanied by a nearly quantized Hall plateau at Landau level filling factor $\nu=4/3$