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Fractional quantum Hall states (FQHSs) at even-denominator Landau level filling factors ($\nu$) are of prime interest as they are predicted to host exotic, topological states of matter. We report here the observation of a FQHS at $\nu=1/2$ in a two-dimensional electron system of exceptionally high quality, confined to a wide AlAs quantum well, where the electrons can occupy multiple conduction-band valleys with an anisotropic effective mass. The anisotropy and multi-valley degree of freedom offer an unprecedented tunability of the $\nu=1/2$ FQHS as we can control both the valley occupancy via the application of in-plane strain, and the ratio between the strengths of the short- and long-range Coulomb interaction by tilting the sample in the magnetic field to change the electron charge distribution. Thanks to this tunability, we observe phase transitions from a compressible Fermi liquid to an incompressible FQHS and then to an insulating phase as a function of tilt angle. We find that this evolution and the energy gap of the $\nu=1/2$ FQHS depend strongly on valley occupancy.

Electrons' multiple quantum degrees of freedom can lead to rich physics, including a competition between various exotic ground states, as well as novel applications such as spintronics and valleytronics. Here we report magneto-transport experiments demonstrating how the valley degree of freedom impacts the fractional quantum states (FQHSs), and the related magnetic-flux-electron composite fermions (CFs), at very high magnetic fields in the extreme quantum limit when only the lowest Landau level is occupied. Unlike in other multivalley two-dimensional electron systems such as Si or monolayer graphene and transition-metal dichalcogenides, in our AlAs sample we can continuously tune the valley polarization via the application of in-situ strain. We find that the FQHSs remain exceptionally strong even as they make valley polarization transitions, revealing a surprisingly robust ferromagnetism of the FQHSs and the underlying CFs. Our observation implies that the CFs are strongly interacting in our system. We are also able to obtain a phase diagram for the FQHS and CF valley polarization in the extreme quantum limit as we monitor transitions of the FHQSs with different valley polarizations.

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 parameter [Formula: see text] , 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 when [Formula: see text] surpasses 35, and then a phase with strongly nonlinear current-voltage characteristics, suggestive of a pinned Wigner solid, when [Formula: see text] exceeds [Formula: see text]. However, our sample makes a transition to an insulating state at [Formula: see text] , 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.

In 1929, Felix Bloch suggested that the paramagnetic Fermi sea of electrons should make a spontaneous transition to a fully magnetized state at very low densities, because the exchange energy gained by aligning the spins exceeds the enhancement in the kinetic energy1. However, experimental realizations of this effect have been hard to implement. Here, we report the observation of an abrupt, interaction-driven transition to full magnetization, highly reminiscent of Bloch ferromagnetism. Our platform utilizes the two-dimensional Fermi sea of composite fermions near half-filling of the lowest Landau level. We measure the Fermi wavevector—which directly provides the spin polarization—and observe a sudden transition from a partially spin-polarized to a fully spin-polarized ground state as we lower the density of the composite fermions. Our theoretical calculations that take Landau level mixing into account provide a semi-quantitative account of this phenomenon. Composite fermions can be tuned to very low effective density in a clean two-dimensional electron gas, which allows the formation of a Bloch ferromagnet.

In a low-disorder two-dimensional electron system, when two Landau levels of opposite spin or pseudospin cross at the Fermi level, the dominance of the exchange energy can lead to a ferromagnetic, quantum Hall ground state whose gap is determined by the exchange energy and has skyrmions as its excitations. This is normally achieved via applying either hydrostatic pressure or uniaxial strain. We study here a very high-quality, low-density, two-dimensional hole system, confined to a 30-nm-wide (001) GaAs quantum well, in which the two lowest-energy Landau levels can be gate tuned to cross at and near filling factor $\nu=1$. As we tune the field position of the crossing from one side of $\nu=1$ to the other by changing the hole density, the energy gap for the quantum Hall state at $\nu=1$ remains exceptionally large, and only shows a small dip near the crossing. The gap overall follows a $\sqrt{B}$ dependence, expected for the exchange energy. Our data are consistent with a robust quantum Hall ferromagnet as the ground state., Comment: 7+2 pages, 4+4 figures

Memory or transistor devices based on an electron's spin rather than its charge degree of freedom offer certain distinct advantages and comprise a cornerstone of spintronics. Recent years have witnessed the emergence of a new field, valleytronics, which seeks to exploit an electron's valley index rather than its spin. An important component in this quest would be the ability to control the valley index in a convenient fashion. Here we show that the valley polarization can be switched from zero to 1 by a small reduction in density, simply tuned by a gate bias, in a two-dimensional electron system. This phenomenon, which is akin to Bloch spin ferromagnetism, arises fundamentally as a result of electron-electron interaction in an itinerant, dilute electron system. Essentially, the kinetic energy favors an equal distribution of electrons over the available valleys, whereas the interaction between electrons prefers single-valley occupancy below a critical density. The gate-bias-tuned transition we observe is accompanied by a sudden, twofold change in sample resistance, making the phenomenon of interest for potential valleytronic transistor device applications. Our observation constitutes a quintessential demonstration of valleytronics in a very simple experiment.

A fundamental concept in physics is the Fermi surface, the constant-energy surface in momentum space encompassing all the occupied quantum states at absolute zero temperature. In 1960, Luttinger postulated that the area enclosed by the Fermi surface should remain unaffected even when electron-electron interaction is turned on, so long as the interaction does not cause a phase transition. Understanding what determines the Fermi surface size is a crucial and yet unsolved problem in strongly interacting systems such as high-$T_{c}$ superconductors. Here we present a precise test of the Luttinger theorem for a two-dimensional Fermi liquid system where the exotic quasi-particles themselves emerge from the strong interaction, namely for the Fermi sea of composite fermions (CFs). Via direct, geometric resonance measurements of the CFs' Fermi wavevector down to very low electron densities, we show that the Luttinger theorem is obeyed over a significant range of interaction strengths, in the sense that the Fermi sea area is determined by the density of the \textit{minority carriers} in the lowest Landau level. Our data also address the ongoing debates on whether or not CFs obey particle-hole symmetry, and if they are Dirac particles. We find that particle-hole symmetry is obeyed, but the measured Fermi sea area differs quantitatively from that predicted by the Dirac model for CFs., 6 pages, 4 figures

A sufficiently large perpendicular magnetic field quenches the kinetic (Fermi) energy of an interacting two-dimensional (2D) system of fermions, making them susceptible to the formation of a Wigner solid (WS) phase in which the charged carriers organize themselves in a periodic array in order to minimize their Coulomb repulsion energy. In low-disorder 2D electron systems confined to modulation-doped GaAs heterostructures, signatures of a magnetic-field-induced WS appear at low temperatures and very small Landau level filling factors ($\nu\simeq1/5$). In dilute GaAs 2D \textit{hole} systems, on the other hand, thanks to the larger hole effective mass and the ensuing Landau level mixing, the WS forms at relatively higher fillings ($\nu\simeq1/3$). Here we report our measurements of the fundamental temperature vs. filling phase diagram for the 2D holes' WS-liquid \textit{thermal melting}. Moreover, via changing the 2D hole density, we also probe their Landau level mixing vs. filling WS-liquid \textit{quantum melting} phase diagram. We find our data to be in good agreement with the results of very recent calculations, although intriguing subtleties remain., Comment: Phys. Rev. Lett. (in press) (2020)

What is the fate of the ground state of a two-dimensional electron system (2DES) at very low Landau level filling factors ($\nu$) where interaction reigns supreme? An ordered array of electrons, the so-called Wigner crystal, has long been believed to be the answer. It was in fact the search for the elusive Wigner crystal that led to the discovery of an unexpected, incompressible liquid state, namely the fractional quantum Hall state at $\nu=1/3$. Understanding the competition between the liquid and solid ground states has since remained an active field of fundamental research. Here we report experimental data for a new two-dimensional system where the electrons are confined to an AlAs quantum well. The exceptionally high quality of the samples and the large electron effective mass allow us to determine the liquid-solid phase diagram for the two-dimensional electrons in a large range of filling factors near $\simeq 1/3$ and $\simeq 1/5$. The data and their comparison with an available theoretical phase diagram reveal the crucial role of Landau level mixing and finite electron layer thickness in determining the prevailing ground states.

Two-dimensional interacting electrons exposed to strong perpendicular magnetic fields generate emergent, exotic quasiparticles phenomenologically distinct from electrons. Specifically, electrons bind with an even number of flux quanta, and transform into composite fermions (CFs). Besides providing an intuitive explanation for the fractional quantum Hall states, CFs also possess Fermi-liquid-like properties, including a well-defined Fermi sea, at and near even-denominator Landau level filling factors such as $��=1/2$ or $1/4$. Here, we directly probe the Fermi sea of the rarely studied four-flux CFs near $��=1/4$ via geometric resonance experiments. The data reveal some unique characteristics. Unlike in the case of two-flux CFs, the magnetic field positions of the geometric resonance resistance minima for $��1/4$ are symmetric with respect to the position of $��=1/4$. However, when an in-plane magnetic field is applied, the minima positions become asymmetric, implying a mysterious asymmetry in the CF Fermi sea anisotropy for $��1/4$. This asymmetry, which is in stark contrast to the two-flux CFs, suggests that the four-flux CFs on the two sides of $��=1/4$ have very different effective masses, possibly because of the proximity of the Wigner crystal formation at small $��$., 7 pages, 4 figures, supplemental materials

The fractional quantum Hall state (FQHS) observed at a half-filled Landau level in an interacting two-dimensional electron system (2DES) is among the most exotic states of matter as its quasiparticles are expected to be Majoranas with non-Abelian statistics. We demonstrate here the unexpected presence of such a state in a novel 2DES with a strong band-mass anisotropy. The FQHS we observe has unusual characteristics. While its Hall resistance is well-quantized at low temperatures, it exhibits highly-anisotropic in-plane transport resembling compressible stripe/nematic charge-density-wave phases. More striking, the anisotropy sets in suddenly below a critical temperature, suggesting a finite-temperature phase transition. Our observations highlight how anisotropy modifies the many-body phases of a 2DES, and should further fuel the discussion surrounding the enigmatic even-denominator FQHS., Comment: Accepted for publication in Phys. Rev. Lett

The enigmatic even-denominator fractional quantum Hall state at Landau level filling factor ν=5/2 is arguably the most promising candidate for harboring Majorana quasiparticles with non-Abelian statistics and, thus, of potential use for topological quantum computing. The theoretical description of the ν=5/2 state is generally believed to involve a topological p-wave pairing of fully-spin-polarized composite fermions through their condensation into a non-Abelian Moore-Read Pfaffian state. There is, however, no direct and conclusive experimental evidence for the existence of composite fermions near ν=5/2 or for an underlying fully-spin-polarized Fermi sea. Here, we report the observation of composite fermions very near ν=5/2 through geometric resonance measurements and find that the measured Fermi wave vector provides direct demonstration of a Fermi sea with full spin polarization. This lends crucial credence to the model of 5/2 fractional quantum Hall effect as a topological p-wave paired state of composite fermions.

Since the discovery of the high-transition-temperature superconductors (HTSs), researchers have explored many methods to fabricate superconducting tunnel junctions from these materials for basic science purposes and applications. HTS circuits operating at liquid-nitrogen temperatures (∼77 K) would significantly reduce power requirements in comparison with those fabricated from conventional superconductors. The difficulty is that the superconducting coherence length is very short and anisotropic in these materials, typically ∼2 nm in the a-b plane and ∼0.2 nm along the c axis. The electrical properties of Josephson junctions are therefore sensitive to chemical variations and structural defects on atomic length scales. To make multiple uniform HTS junctions, control at the atomic level is required. In this Letter we demonstrate all-HTS Josephson superconducting tunnel junctions created by using a 500-pm-diameter focused beam of helium ions to directly write tunnel barriers into YBa2Cu3O(7-δ) (YBCO) thin films. We demonstrate the ability to control the barrier properties continuously from conducting to insulating by varying the irradiation dose. This technique could provide a reliable and reproducible pathway for scaling up quantum-mechanical circuits operating at liquid-nitrogen temperatures, as well as an avenue to conduct novel planar superconducting tunnelling studies for basic science.

The enigmatic even-denominator fractional quantum Hall state at Landau level filling factor ν=5/2 is arguably the most promising candidate for harboring Majorana quasiparticles with non-Abelian statistics and, thus, of potential use for topological quantum computing. The theoretical description of the ν=5/2 state is generally believed to involve a topological p-wave pairing of fully-spin-polarized composite fermions through their condensation into a non-Abelian Moore-Read Pfaffian state. There is, however, no direct and conclusive experimental evidence for the existence of composite fermions near ν=5/2 or for an underlying fully-spin-polarized Fermi sea. Here, we report the observation of composite fermions very near ν=5/2 through geometric resonance measurements and find that the measured Fermi wave vector provides direct demonstration of a Fermi sea with full spin polarization. This lends crucial credence to the model of 5/2 fractional quantum Hall effect as a topological p-wave paired state of composite fermions.

The interplay between different orders is of fundamental importance in physics. The spontaneous, symmetry-breaking charge order, responsible for the stripe or the nematic phase, has been of great interest in many contexts where strong correlations are present, such as high-temperature superconductivity and quantum Hall effect. In this article we show the unexpected result that in an interacting two-dimensional electron system, the robustness of the nematic phase, which represents an order in the charge degree of freedom, not only depends on the orbital index of the topmost, half-filled Landau level, but it is also strongly correlated with the magnetic order of the system. Intriguingly, when the system is fully magnetized, the nematic phase is particularly robust and persists to much higher temperatures compared to the nematic phases observed previously in quantum Hall systems. Our results give fundamental new insight into the role of magnetization in stabilizing the nematic phase, while also providing a new knob with which it can be effectively tuned.

The two-dimensional electron system in an InAs quantum well has emerged as a prime candidate for hosting exotic quasiparticles 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 the 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 $n=7.8\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$ and low-temperature mobility $1.8\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{2}$/Vs. At a temperature of $\ensuremath{\simeq}\phantom{\rule{0.16em}{0ex}}35$ mK and $B\ensuremath{\simeq}24$ T, we observe a deep minimum in the longitudinal resistance, accompanied by a nearly quantized Hall plateau at a Landau level filling factor $\ensuremath{\nu}=4/3$.

In this work, we demonstrate the ability to fabricate superconducting quantum interference devices (SQUIDs) by directly writing Josephson junctions into the plane of YBa2Cu3O7−δ thin films with a focused helium ion beam. This technique allows for the control of the Josephson barrier transport properties through the single parameter, ion dose. SQUIDs written with a dose of 4 × 1016 ions/cm2 had metallic barrier junctions that exhibited nearly ideal electrical transport characteristics at 50 K and a flux noise of 20 μΦ0/Hz at 10 Hz. At higher irradiation doses, the SQUIDs had insulating barrier Josephson junctions with a quasi particle energy gap edge at 20 meV.