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.
Composite fermions (CFs), exotic particles formed by pairing an even number of flux quanta to each electron, provide a fascinating description of phenomena exhibited by interacting two-dimensional ...electrons at high magnetic fields. At and near Landau level filling ν=1/2, CFs occupy a Fermi sea and exhibit commensurability effects when subjected to a periodic potential modulation. We observe a pronounced asymmetry in the magnetic field positions of the commensurability resistance minima of CFs with respect to the field at ν=1/2. This unexpected asymmetry is consistent with the CFs' Fermi wave vector being determined by the minority carriers in the lowest Landau level, and suggests a breaking of the particle-hole symmetry for CFs near ν=1/2.
In two-dimensional electron systems confined to GaAs quantum wells, as a function of either tilting the sample in a magnetic field or increasing density, we observe multiple spin-polarization ...transitions of the fractional quantum Hall states at filling factors ν=4/5 and 5/7. The number of observed transitions provides evidence that these are fractional quantum Hall states of interacting two-flux composite fermions. Moreover, the fact that the reentrant integer quantum Hall effect near ν=4/5 always develops following the transition to full spin polarization of the ν=4/5 fractional quantum Hall state links the reentrant phase to a pinned ferromagnetic Wigner crystal of composite fermions.
Disorder and electron-electron interaction play essential roles in the physics of electron systems in condensed matter. In two-dimensional, quantum Hall systems, extensive studies of disorder-induced ...localization have led to the emergence of a scaling picture with a single extended state, characterized by a power-law divergence of the localization length in the zero-temperature limit. Experimentally, scaling has been investigated via measuring the temperature dependence of plateau-to-plateau transitions between the integer quantum Hall states (IQHSs), yielding a critical exponent κ≃0.42. Here we report scaling measurements in the fractional quantum Hall state (FQHS) regime where interaction plays a dominant role. Our Letter is partly motivated by recent calculations, based on the composite fermion theory, that suggest identical critical exponents in both IQHS and FQHS cases to the extent that the interaction between composite fermions is negligible. The samples used in our experiments are two-dimensional electron systems confined to GaAs quantum wells of exceptionally high quality. We find that κ varies for transitions between different FQHSs observed on the flanks of Landau level filling factor ν=1/2 and has a value close to that reported for the IQHS transitions only for a limited number of transitions between high-order FQHSs with intermediate strength. We discuss possible origins of the nonuniversal κ observed in our experiments.
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 Tc superconductors. Here we present a precise test of the Luttinger theorem for a two-dimensional Fermi liquid system where the exotic quasiparticles themselves emerge from the strong interaction, namely, for the Fermi sea of composite fermions (CFs). Via direct, geometric resonance measurements of the CFs' Fermi wave vector 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 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.
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 rs
, 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 rs
surpasses 35, and then a phase with strongly nonlinear current-voltage characteristics, suggestive of a pinned Wigner solid, when rs
exceeds ≃38. However, our sample makes a transition to an insulating state at rs
≃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.
Understanding the flow of spins in magnetic layered structures has resulted in an increase in data storage density in hard drives over the past decade of more than two orders of magnitude. Following ...this remarkable success, the field of 'spintronics' or spin-based electronics is moving beyond effects based on local spin polarization and is turning towards 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. Although 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. We first introduce the class of phenomena we dub 'the one-dimensional spin-orbit gap' using a simple example adapted from ref. 10, then describe our experiment in detail and finally present a more elaborate model that captures most of the features seen in our data.
Topological physics relies on the structure of the eigenstates of the Hamiltonians. The geometry of the eigenstates is encoded in the quantum geometric tensor
-comprising the Berry curvature
(crucial ...for topological matter)
and the quantum metric
, which defines the distance between the eigenstates. Knowledge of the quantum metric is essential for understanding many phenomena, such as superfluidity in flat bands
, orbital magnetic susceptibility
, the exciton Lamb shift
and the non-adiabatic anomalous Hall effect
. However, the quantum geometry of energy bands has not been measured. Here we report the direct measurement of both the Berry curvature and the quantum metric in a two-dimensional continuous medium-a high-finesse planar microcavity
-together with the related anomalous Hall drift. The microcavity hosts strongly coupled exciton-photon modes (exciton polaritons) that are subject to photonic spin-orbit coupling
from which Dirac cones emerge
, and to exciton Zeeman splitting, breaking time-reversal symmetry. The monopolar and half-skyrmion pseudospin textures are measured using polarization-resolved photoluminescence. The associated quantum geometry of the bands is extracted, enabling prediction of the anomalous Hall drift, which we measure independently using high-resolution spatially resolved epifluorescence. Our results unveil the intrinsic chirality of photonic modes, the cornerstone of topological photonics
. These results also experimentally validate the semiclassical description of wavepacket motion in geometrically non-trivial bands
. The use of exciton polaritons (interacting photons) opens up possibilities for future studies of quantum fluid physics in topological systems.
The single-particle spectral function measures the density of electronic states in a material as a function of both momentum and energy, providing central insights into strongly correlated electron ...phenomena. Here we demonstrate a high-resolution method for measuring the full momentum- and energy-resolved electronic spectral function of a two-dimensional (2D) electronic system embedded in a semiconductor. The technique remains operational in the presence of large externally applied magnetic fields and functions even for electronic systems with zero electrical conductivity or with zero electron density. Using the technique on a prototypical 2D system, a GaAs quantum well, we uncover signatures of many-body effects involving electron-phonon interactions, plasmons, polarons, and a phonon analog of the vacuum Rabi splitting in atomic systems.
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