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DOE OSTI2023

Low-field magnetic anomalies in single crystals of the A-type square-lattice antiferromagnet EuGa 4

The body-centered-tetragonal antiferromagnet EuGa 4 was recently identified as a Weyl nodal-line semimetal that exhibits the topological Hall effect below its reported antiferromagnetic (AFM) ordering temperature T N = 15 – 16.5 K which we find to be T N = 16.4 ( 2 ) K. The Eu +2 ions are located at the corners and body centers of the unit cells. EuGa 4 exhibits A-type antiferromagnetic order below T N , where the Eu 2+ spin-7/2 moments are ferromagnetically aligned in the ab plane with the Eu moments in adjacent Eu planes along the c axis aligned antiferromagnetically. Low-field magnetization versus field M(H ab ) data at T = 2 K with the field aligned in the ab plane are reported that exhibit anomalous positive curvature up to a critical field H c1 at which a second-order transition occurs with H c1 ≈ 0.85 kOe for H∥ [1,1,0] and ≈ 4.8 kOe for H∥[1,0,0]. For larger fields, the linear behavior M ab = χ(T N ) H a b is followed until the critical field H c is reached at which all moments become aligned with the applied field. A theory is formulated for T = 0 K that fits the observed M(H ab ) behavior at T = 2 K well, where domains of A -type AFM order with fourfold rotational symmetry occur in the AFM state in zero field. The moments in the four domains reorient to become almost perpendicular to H ab at H c1 , followed by increasing canting of all moments toward the field with increasing field up to H c which is reported to be 71 kOe. A first-order transition in M(H ab ) at H ab = H c1 is predicted by the theory for T = 0 K when H ab is at a small angle from the [1,0,0] direction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Physics of E × B discharges relevant to plasma propulsion and similar technologies

This paper provides perspectives on recent progress in understanding the physics of devices in which the external magnetic field is applied perpendicular to the discharge current. This configuration generates a strong electric field that acts to accelerate ions. The many applications of this set up include generation of thrust for spacecraft propulsion and separation of species in plasma mass separation devices. These “E × B” plasmas are subject to plasma–wall interaction effects and to various micro- and macroinstabilities. In many devices we also observe the emergence of anomalous transport. This perspective presents the current understanding of the physics of these phenomena and state-of-the-art computational results, identifies critical questions, and suggests directions for future research.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1993

Anode power deposition in magnetoplasmadynamic thrusters

Results of anode heat-flux and anode fail measurements from a multimegawatt self-field quasi-steady magnetoplasmadynamic (MPD) thruster are presented. Measurements were obtained with argon and helium propellants for a variety of currents and mass flow rates. Anode heat flux was directly measured with thermocouples attached to the inner surface of a hollowed section. Anode falls were determined both from floating probes and through heat flux measurements. Comparison of data acquired through either method shows excellent agreement. Anode falls varied between 4-50 V with anode power fractions reaching 70 percent with helium at 150 kW, and 50 percent with argon at 1.9 MW. The anode fall was found to correlate well with electron Hall parameters calculated from triple Langmuir and magnetic probe data collected near the anode. Two possible explanations for this result are proposed: (1) the establishment of large electric fields at the anode to maintain current conduction across the strong magnetic fields; and (2) anomalous resistivity resulting from the onset of microturbulence in the plasma. To investigate the latter hypothesis, electric field, magnetic field, and current density profiles measured in the vicinity of the anode were incorporated into Ohm's law to estimate the electrical conductivity. Results of this analysis show a substantial deviation of the measured conductivity from that calculated with classical formulas. These results imply that anomalous effects are present in the plasma near the anode.

Gallimore, A. D.↗

DOE OSTI2025

Hetero-Orbital Two-Component Fractional Quantum Hall States in Bilayer Graphene

A two-dimensional electron system exposed to a strong magnetic field produces a plethora of strongly interacting fractional quantum Hall (FQH) states, the complex topological orders of which are revealed through exotic emergent particles, such as composite fermions, and fractionally charged Abelian and non-Abelian anyons. Much insight has been gained by the study of multicomponent FQH states, where spin and pseudospin indices of the electron contribute additional correlation. Traditional multicomponent FQH states develop in situations where the components share the same orbital states and the resulting interactions are pseudospin independent; this homo-orbital nature is also crucial to their theoretical understanding. Here, we study “hetero-orbital” two-component FQH states, in which the orbital index is part of the pseudospin, rendering the multicomponent interactions strongly SU(2) anisotropic in the pseudospin space. Such states, obtained in bilayer graphene at the isospin transition between 𝑁 = 0 and 𝑁 = 1 electron Landau levels, are markedly different from previous homo-orbital two-component FQH states. In particular, we observe strikingly different behaviors for the parallel-vortex and reverse-vortex attachment composite fermion states, and an anomalously strong two-component 2/5 state over a wide range of magnetic field before it abruptly disappears at a high field. Our findings, combined with detailed theoretical calculations, reveal the surprising robustness of the hetero-orbital FQH effects, significantly enriching our understanding of FQH physics in this novel regime.

Bilayer graphene↗

DOE OSTI2020

Magnetic asymmetry induced anomalous spin-orbit torque in IrMn

We demonstrate an anomalous spin-orbit torque induced by the broken magnetic symmetry in the antiferromagnet IrMn. We study the magnetic structure of three phases of IrMn thin films using neutron diffraction technique. The magnetic mirror symmetry M ' is broken laterally in both L 1 0 - IrMn and L 1 2 - IrM n 3 but not γ - IrM n 3 . We observe an out-of-plane dampinglike spin-orbit torque in both L 1 0 - IrMn /permalloy and L 1 2 - IrM n 3 /permalloy bilayers but not in γ - IrM n 3 /permalloy. This is consistent with both the symmetry analysis on the effects of a broken M ' on spin-orbit torque and the theoretical predictions of the spin Hall effect and the Rashba-Edelstein effect. In addition, the measured spin-orbit torque efficiencies are 0.61 ± 0.01, 1.01 ± 0.03, and 0.80 ± 0.01 for the L 1 0 , L 1 2 , and γ phases, respectively. Our work highlights the critical roles of the magnetic asymmetry in spin-orbit torque generation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS2014

A New Cell-Centered Implicit Numerical Scheme for Ions in the 2-D Axisymmetric Code Hall2de

We present a new algorithm in the Hall2De code to simulate the ion hydrodynamics in the acceleration channel and near plume regions of Hall-effect thrusters. This implementation constitutes an upgrade of the capabilities built in the Hall2De code. The equations of mass conservation and momentum for unmagnetized ions are solved using a conservative, finite-volume, cell-centered scheme on a magnetic-field-aligned grid. Major computational savings are achieved by making use of an implicit predictor/multi-corrector algorithm for time evolution. Inaccuracies in the prediction of the motion of low-energy ions in the near plume in hydrodynamics approaches are addressed by implementing a multi-fluid algorithm that tracks ions of different energies separately. A wide range of comparisons with measurements are performed to validate the new ion algorithms. Several numerical experiments with the location and value of the anomalous collision frequency are also presented. Differences in the plasma properties in the near-plume between the single fluid and multi-fluid approaches are discussed. We complete our validation by comparing predicted erosion rates at the channel walls of the thruster with measurements. Erosion rates predicted by the plasma properties obtained from simulations replicate accurately measured rates of erosion within the uncertainty range of the sputtering models employed.

electric propulsion↗

DOE OSTI2025

Signatures of chiral superconductivity in rhombohedral graphene

Chiral superconductors are unconventional superconducting states that break time-reversal symmetry spontaneously and typically feature Cooper pairing at non-zero angular momentum. Such states may host Majorana fermions and provide an important platform for topological physics research and fault-tolerant quantum computing. Despite intensive search and prolonged studies of several candidate systems, chiral superconductivity has remained elusive so far. Here we report the discovery of robust unconventional superconductivity in rhombohedral tetralayer and pentalayer graphene without moiré superlattice effects. We observed two superconducting states in the gate-induced flat conduction bands with T c up to 300 mK and charge density n e down to 2.4 ×10 11 cm −2 in five devices. Spontaneous time-reversal-symmetry breaking (TRSB) owing to orbital motion of the electron is found and several observations indicate the chiral nature of these superconducting states, including: (1) in the superconducting state, R xx shows magnetic hysteresis in varying out-of-plane magnetic field B ⊥ —absent from all other superconductors; (2) the superconducting states are robust against in-plane magnetic field and are developed within a spin-polarized and valley-polarized quarter-metal (QM) phase; (3) the normal states show anomalous Hall signals at zero magnetic field and magnetic hysteresis. Here, we also observed a critical B ⊥ of 1.4 T, higher than any graphene superconductivity, which indicates a strong-coupling superconductivity close to the Bardeen–Cooper–Schrieffer (BCS)–Bose–Einstein condensate (BEC) crossover. Our observations establish a pure carbon material for the study of topological superconductivity, with the promise to explore Majorana modes and topological quantum computing.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Dimensional Control of Octahedral Tilt in SrRuO 3 via Infinite-Layered Oxides

Manipulation of octahedral distortion at atomic scale is an effective means to tune the ground states of functional oxides. Previous work demonstrates that strain and film thickness are variable parameters to modify the octahedral parameters. However, selective control of bonding geometry by structural propagation from adjacent layers is rarely studied. Here we propose a new route to tune the ferromagnetism in SrRuO 3 (SRO) ultrathin layers by oxygen coordination of adjacent SrCuO 2 (SCO) layers. The infinite-layered CuO 2 exhibits a structural transformation from “planar-type” to “chain-type” with reduced film thickness. Two orientations dramatically modify the polyhedral connectivity at the interface, thus altering the octahedral distortion of SRO. The local structural variation changes the spin state of Ru and orbital hybridization strength, leading to a significant change in the magnetoresistance and anomalous Hall resistivity. Furthermore, these findings could launch investigations into adaptive control of functionalities in quantum oxide heterostructures using oxygen coordination.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Anomalous magnetothermoelectric behavior in massive Dirac materials

Extensive studies of electron transport in Dirac materials have shown positive magnetoresistance (MR) and positive magnetothermopower (MTP) in a magnetic field perpendicular to the excitation current or thermal gradient. In contrast, measurements of electron transport often show a negative longitudinal MR and negative MTP for a magnetic field oriented along the excitation current or thermal gradient; this is attributed to the chiral anomaly in Dirac materials. In this paper, we report a very different magnetothermoelectric transport behavior in the massive Dirac material ZrTe5. Although thin flakes show a commonly observed positive MR in a perpendicular magnetic field, distinct from other Dirac materials, we observe a sharp negative MTP. In a parallel magnetic field, we still observe a negative longitudinal MR, however, a remarkable positive MTP is observed for the fields parallel to the thermal gradients. Our theoretical calculations suggest that this anomalous magnetothermoelectric behavior can be attributed to the screened Coulomb scattering. This work demonstrates the significance of impurity scattering in the electron transport of topological materials and provides deep insight into the magnetotransport phenomena in Dirac materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Nernst power factor and figure of merit in the compensated semimetal ScSb

Recently, topological semimetals have emerged as strong candidates for solid-state thermomagnetic refrigerators due to their enhanced Nernst effect. This enhancement arises from the combined contributions of the Berry-curvature-induced anomalous Nernst coefficient associated with topological bands and the normal Nernst effect resulting from synergistic electron-hole compensation. Generally, these two effects are intertwined in topological semimetals, making it challenging to evaluate them independently. Here, we report the observation of a high Nernst effect in the electron-hole compensated semimetal ScSb with topologically trivial electronic band structures. Remarkably, we find a high maximum Nernst power factor of 𝑃⁢𝐹 𝑁 ∼ 35 × 10 −4 W m −1 K −2 in ScSb. The Nernst thermopower (𝑆 𝑥⁢𝑦 ) exhibits a peak of ∼ 47 µ⁢V/K at 12 K and 14 T, yielding a Nernst figure of merit (𝑧 𝑁 ) of ∼ 28 × 10 −4 K −1 . Notably, despite its trivial electronic band structure, both the 𝑃⁢𝐹 𝑁 and 𝑧 𝑁 values of ScSb are comparable to those observed in topological semimetals with Dirac band dispersions. In conclusion, the origin of the large Nernst signal in ScSb is explained by compensated electron and hole carriers, through Hall resistivity measurements, angle-resolved photoemission spectroscopy, and density functional theory calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1998

The Sound Parameter Effect in Metal-Rich Globular Clusters

Recent Hubble Space Telescope observations have found that the horizontal branches (HBs) in the metal-rich globular clusters NGC 6388 and NGC 6441 slope upward with decreasing B - V. Such a slope is not predicted by canonical HB models and cannot be produced by either a greater cluster age or enhanced mass loss along the red giant branch (RGB). The peculiar HB morphology in these clusters may provide an important clue for understanding the second-parameter effect. We have carried out extensive evolutionary calculations and numerical simulations in order to explore three noncanonical scenarios for explaining the sloped HBs in NGC 6388 and NGC 6441: (1) a high cluster helium abundance scenario, in which the HB evolution is characterized by long blue loops; (2) a rotation scenario, in which internal rotation during the RGB phase increases the HB core mass; and (3) a helium-mixing scenario, in which deep mixing on the RGB enhances the envelope helium abundance. All of these scenarios predict sloped HBs with anomalously bright RR Lyrae variables. We compare this prediction with the properties of the two known RR Lyrae variables in NGC 6388. Additional observational tests of these scenarios are suggested.

Hall, D. K↗

DOE OSTI2020

Combining Spin-Seebeck and Nernst Effects in Aligned MnBi/Bi Composites

The spin-Seebeck effect (SSE) is an advective transport process traditionally studied in bilayers composed of a ferromagnet (FM) and a non-magnetic metal (NM) with strong spin-orbit coupling. In a temperature gradient, the flux of magnons in the FM transfers spin-angular momentum to electrons in the NM, which by the inverse spin-Hall effect generates an SSE voltage. In contrast, the Nernst effect is a bulk transport phenomenon in homogeneous NMs or FMs. These effects share the same geometry, and we show here that they can be added to each other in a new combination of FM/NM composites where synthesis via in-field annealing results in the FM material (MnBi) forming aligned needles inside an NM matrix with strong spin-orbit coupling (SOC) (Bi). Through examination of the materials’ microstructural, magnetic, and transport properties, we searched for signs of enhanced transverse thermopower facilitated by an SSE contribution from MnBi adding to the Nernst effect in Bi. Our results indicate that these two signals are additive in samples with lower MnBi concentrations, suggesting a new way forward in the study of SSE composite materials.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Geometric origin of the intrinsic transverse spin transport in a canted-antiferromagnet/heavy-metal heterostructure

We theoretically study the conditions under which an intrinsic spin Nernst effect–a transverse spin current induced by an applied temperature gradient–can occur in a canted-antiferromagnet insulator, such as LaFeO 3 and other materials of the same family. The spin Nernst effect may provide a microscopic mechanism for an experimentally observed anomalous thermovoltage in LaFeO 3 /Pt heterostructures, where spin is transferred across the insulator/metal interface when a temperature gradient is applied to LaFeO 3 parallel to the interface. We find that LaFeO 3 exhibits an intrinsic spin Nernst effect when inversion symmetry is broken on the axes parallel to both the applied temperature gradient and the direction of spin transport, which can result in a spin injection across the insulator/metal interface. Furthermore, our paper provides a general derivation of a symmetry-breaking-induced spin Nernst effect, which may open a path to engineering a finite spin Nernst effect in systems where it would otherwise not arise.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice

Studies of two-dimensional electron systems in a strong magnetic field revealed the quantum Hall effect, a topological state of matter featuring a finite Chern number C and chiral edge states. Haldane later theorized that Chern insulators with integer quantum Hall effects could appear in lattice models with complex hopping parameters even at zero magnetic field. The ABC-trilayer graphene/hexagonal boron nitride (ABC-TLG/hBN) moiré superlattice provides an attractive platform with which to explore Chern insulators because it features nearly flat moiré minibands with a valley-dependent, electrically tunable Chern number. In this work, we report the experimental observation of a correlated Chern insulator in an ABC-TLG/hBN moiré superlattice. We show that reversing the direction of the applied vertical electric field switches the moiré minibands of ABC-TLG/hBN between zero and finite Chern numbers, as revealed by large changes in magneto-transport behaviour. For topological hole minibands tuned to have a finite Chern number, we focus on quarter filling, corresponding to one hole per moiré unit cell. The Hall resistance is well quantized at h/2e 2 (where h is Planck’s constant and e is the charge on the electron), which implies C = 2, for a magnetic field exceeding 0.4 tesla. The correlated Chern insulator is ferromagnetic, exhibiting substantial magnetic hysteresis and a large anomalous Hall signal at zero magnetic field. Finally, our discovery of a C = 2 Chern insulator at zero magnetic field should open up opportunities for discovering correlated topological states, possibly with topological excitations, in nearly flat and topologically nontrivial moiré minibands.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Searches for New Physics With Muon Conversion at Fermilab and Triboson Production at the LHC

We report on several efforts to search for physics beyond the standard model of particle physics at broad energy scales. The Mu2e experiment at Fermilab will search for charged lepton flavor violation via the muon to electron conversion process, which is suppressed in the Standard Model. Mu2e will be operated at a low energy, yet can probe New Physics at very high mass scales (O(1e3 - 1e4 ) TeV). At high energies, the CMS experiment at the CERN LHC continues to deliver an impressive suite of Standard Model measurements and limits on a variety of New Physics signatures. Mu2e is under construction and slated to collect its first physics data in the coming years. This thesis describes work done during the construction phase of Mu2e and focuses on two critical areas: magnetic field modeling and statistical analysis. We describe a novel method for field modeling which we validate using a simulated dataset representing the expected magnetic field in the Detector Solenoid. This method blends a standard least-squares fitting technique that utilizes physically motivated analytical model functions with a novel physics informed network that is constructed to obey Maxwell’s equations. We show the technique can model the field with an accuracy of 10−7 despite the presence of injected noise in the pseudo-measurements at the 10−5 level. We then present preliminary results of the calibration of 3D Hall probes at the sub-10−4 level. These probes will be used to directly measure the Mu2e Detector Solenoid magnetic field on a sparse grid; these measurements serve as the input to the field model fitting. Finally, we describe the first implementation of both an unbinned shape analysis and a Bayesian interpretation applied to Mu2e pseudo-data. Up to 20% tighter limits can be set by the shape analysis compared to a standard cut & count analysis. The AlCap experiment collected data at PSI in 2015 to measure several important quantities related to nuclear muon capture on an aluminum target, which is a significant background process for Mu2e. The neutron emission from muon capture can introduce background hits in the Mu2e detectors and can increase radiation damage in various elements of the apparatus. We present measurements of the neutron group fluence and mean neutron multiplicity for muon capture on aluminum nuclei. Finally, we discuss an analysis of triboson production at CMS using an Effective Field Theory framework. Standard Model triboson production, which was first observed at CMS in 2020, has a relatively small cross section and provides direct access to both anomalous triple gauge couplings and quartic gauge couplings. These couplings, interpreted in the Standard Model Effective Field Theory, are studied in the present work. We target the boosted regime where the background rate is low and yields are enhanced when dimension-6 and dimension-8 Wilson coefficients are non-zero. We do not observe an excess in the data and therefore set bounds on the Wilson coefficients. For dimension-6 coefficients the tightest observed (expected) bounds are set on cW /Λ2 where Λ is the mass scale of new physics; the bounds are [−0.13, 0.12] TeV−2 ([−0.12, 0.12] TeV−2 ) at 95% CL. The tightest bounds in dimension-8 are set on fT,0 / Λ4 ; the observed (expected) bounds at 95% CL are [−0.63, 0.69] TeV−4 ([−0.54, 0.62] TeV−4 ). Additional results are presented which include scenarios where multiple Wilson coefficients are non-zero, the application of signal model clipping to address unitarity violation in Effective Field Theories, and a novel template fit developed for easier reinterpretation of our results.

Kampa, Cole Erik [Northwestern U. (main)] (ORCID:0↗

NASA NTRS2020

Cross-field Streaming Instabilities in the Lower Hybrid Frequency Near the Front Pole Regions of a Magnetically Shielded Hall Thruster

The mechanism that led to the erosion of the inner front pole cover in wear tests of the Hall-effect Rocket with Magnetic Shielding (HERMeS) at 300 V and 12.5 kW has been elusive. Several classical mechanisms have been considered yet none has explained conclusively the source of the discrepancy between wear measurements and simulations. In this article we consider a new mechanism. The electrostatic dispersion relation for an unbounded, homogeneous plasma in a fixed magnetic field is solved numerically in the near-plume region of this thruster. The plasma conditions have been obtained from Hall2De (r-z) multifluid-PIC simulations. We find that the modified two-stream instability can be excited in most regions of the domain, with the fastest growth approaching the fluid-limit value of ωLH/2 near the magnetic poles where ωpe/ωce~1. In this region the relative drift between magnetized electrons and beam ions perpendicular to the magnetic field can exceed 3uTi, while that between counter-streaming beam and cathode ions can exceed 4uTi. The latter suggests that the ion-ion cross-field lower hybrid instability may also be active here. Unlike the classical ion-acoustic instability, lower hybrid instabilities can heat ions to temperatures that are comparable to the electron temperature. Such anomalous heating would enhance the average energy of these ions and, in turn, the erosion of the nearby surfaces they sputter. An idealized model that scales the anomalous ion heating with ωLH has been incorporated in Hall2De and the simulations now yield significantly improved agreement with the measured wear rates and IVDFs, as reported in our companion paper.

Ortega, Alejandro Lopez↗

NASA NTRS2008

Preliminary Results of Performance Measurements on a Cylindrical Hall-Effect Thruster with Magnetic Field Generated by Permanent Magnets

The performance of a low-power cylindrical Hall thruster, which more readily lends itself to miniaturization and low-power operation than a conventional (annular) Hall thruster, was measured using a planar plasma probe and a thrust stand. The field in the cylindrical thruster was produced using permanent magnets, promising a power reduction over previous cylindrical thruster iterations that employed electromagnets to generate the required magnetic field topology. Two sets of ring-shaped permanent magnets are used, and two different field configurations can be produced by reorienting the poles of one magnet relative to the other. A plasma probe measuring ion flux in the plume is used to estimate the current utilization for the two magnetic configurations. The measurements indicate that electron transport is impeded much more effectively in one configuration, implying a higher thrust efficiency. Preliminary thruster performance measurements on this configuration were obtained over a power range of 100-250 W. The thrust levels over this power range were 3.5-6.5 mN, with anode efficiencies and specific impulses spanning 14-19% and 875- 1425 s, respectively. The magnetic field in the thruster was lower for the thrust measurements than the plasma probe measurements due to heating and weakening of the permanent magnets, reducing the maximum field strength from 2 kG to roughly 750-800 G. The discharge current levels observed during thrust stand testing were anomalously high compared to those levels measured in previous experiments with this thruster.

Polzin, K. A.↗

DOE OSTI2026

Pathways from a chiral superconductor to a composite Fermi liquid

Recent experiments have reported chiral time-reversal broken superconductivity in n-layer rhombohedral graphene for n=4,5,6. Introducing a moiré potential by alignement with a hexagonal boron nitride substrate suppresses the superconductivity but leads instead to various fractional quantum anomalous Hall phenomena. Motivated by these observations, we consider the fate of the phase transition between (a chiral) Landau Fermi liquid (LFL) metal and a Composite Fermi Liquid (CFL) metal in the presence of attractive interactions. These are parent states, respectively, for the superconductor and the fractional quantum Hall states. For weak attractive interactions, the LFL is usually unstable to superconductivity while the CFL is stable. This raises the possibility of a direct continuous phase transition between the chiral superconductor and the CFL. However, we show that generically the LFL close to the transition to the CFL is stable against superconductivity. Furthermore the evolution between the CFL and chiral superconductor goes through an intermediate stable LFL phase for weak attractive interactions. With stronger interactions, the evolution can instead go through a non-Abelian paired quantum Hall state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗