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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Thermal activation signatures of the Anderson insulator and the Wigner solid forming near ν = 1

When interactions overcome disorder, integer quantum Hall plateaus support topological phases with different bulk insulators. In the center of the ν = 1 plateau the bulk is an Anderson-type insulator, while in the flanks of the plateau the bulk is the integer quantum Hall Wigner solid. We find that the activation energy along the ν = 1 plateau exhibits a very dramatic nonmonotonic dependence on the magnetic field, a dependence that is strongly correlated with the stability regions of the two phases. Furthermore, the activation energy has an unexpected minimum at the boundary between the Anderson insulator and the Wigner solid. Our findings constrain the theory of the integer quantum Hall Wigner solid, determine its thermodynamic properties, and reveal unusual behavior at the boundary between the Anderson insulator and the Wigner solid. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Excitons in fractionally filled moiré superlattices

Long-range Coulomb forces give rise to correlated insulating states when charge particles populate a moiré superlattice at certain fractional filling factors. Such behavior is characterized by a broken translation symmetry wherein particles spontaneously form a Wigner crystal. Here, focusing on the experimental findings of Xu et al. [Nature (London) 587, 214 (2020)], we present a theory that captures the correlated insulating state of a fractionally filled moiré superlattice through the energy shift and change in oscillator strength of the exciton absorption resonance. The theory shows that the experimental findings can only be supported if the electrons reside in a charge-ordered state (i.e., electrons are not randomly distributed among the sites of the moiré superlattice). Furthermore, we explain why the energy shifts of exciton resonances are qualitatively different in cases where the superlattice is nearly empty compared with a superlattice whose sites are doubly occupied.

excitons↗
DOE OSTI2024

Electron confinement–induced plasmonic breakdown in metals

Plasmon resonance represents the collective oscillation of free electron gas density and enables enhanced light-matter interactions in nanoscale dimensions. Traditionally, the classical Drude model describes plasmonic excitation, wherein plasma frequency exhibits no spatial dispersion. Here, we show conclusive experimental evidence of the breakdown of plasmon resonance and a consequent metal-insulator transition in an ultrathin refractory plasmonic material, hafnium nitride (HfN). Epitaxial HfN thick films exhibit a low-loss and high-quality Drude-like plasmon resonance in the visible spectral range. However, as the film thickness is reduced to nanoscale dimensions, Coulomb interaction among electrons increases because of electron confinement, leading to the spatial dispersion of plasma frequency. With a further decrease in thickness, electrons lose their ability to shield the incident electric field, turning the medium into a dielectric. The observed metal-insulator transition might carry some signatures of Wigner crystallization and indicates that such transdimensional, between 2D and 3D, films can serve as a promising playground to study strongly correlated electron systems.

Science & Technology - Other Topics↗
DOE OSTI2023

Novel X-Ray Probes of Electronically Heterogeneous Quantum Materials

The goal of this research was to advance the use of resonant soft x-ray scattering (RSXS) by deepening our theoretical understanding of the technique and expanding its use to a wide range of materials. Under this award, we showed how RSXS techniques can be applied to oxide heterostructures, studied commensuration effects in Wigner crystals, discovered a charge density wave in nickel-arsenide superconductors, and measured time-resolved dynamics of charge order in copper-oxide superconductors, among many other achievements. This award contributed to adoption of RSXS techniques by researchers around the nation and the world.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Microwave and rf Spectroscopy of 2D Carrier Systems and Bilayers (Final Technical Report)

We performed microwave spectroscopic studies of two dimensional electron systems (2DES) exhibiting the quantum Hall effect (QHE) in GaAs/Al${_x}$Ga$_{1-x}$As heterostructures. A common theme of the proposed work is electron solids, of which the simplest is the Wigner crystal, a triangular lattice of individual carriers. The solids are stabilized by carrier-carrier interaction and occur under conditions when the kinetic energy of the system is "frozen out" by high magnetic field, $B$. One of the main reasons for microwave spectroscopic study of 2DES is that the solid phases have striking microwave or rf spectra. In the low wave vector ($q$) limit these spectra exhibit a resonance that is understood as a pinning mode, a small collective oscillation of pieces of the solid within the disorder potential. Pinning modes can be very sharp, with quality factors up to around 30, and are valuable as signatures of the electron solids, and can reveal a solid even when standard dc transport shows an insulator, an integer QHE, or even a fractional QHE The pinning mode also is sensitive to the solid properties, and can reveal transitions between solids.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Novel quantum states of matter in moiré materials (2023 Aspen Winter Conference)

This report is to summarize the proceedings of the conference “Novel Quantum States of Matter in Moiré Materials,” which was held at the Aspen Center for Physics, March 12 – 17, 2023. The conference organizers thank the Department of Energy (DOE) for providing funding support for the conference. The advent of moiré quantum materials has opened a highly tunable platform for exploring the interplay between electronic structure, interactions, symmetry, and topology. Since the discovery of correlated insulator states and superconductivity in magic-angle twisted bilayer graphene (MATBG), a growing variety of moiré systems have emerged, revealing novel correlated and topological phenomena such as quantum anomalous Hall systems, generalized Wigner crystals, and fractional Chern insulators. This rich phenomenology continues to attract intense theoretical and experimental interest.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Correlated States of Two-dimensional Electron Systems in AlAs Quantum Wells

Two-dimensional (2D) carrier systems confined to modulation-doped semiconductor hetero-structures provide a nearly ideal testing ground for exploring new physical phenomena. At low temperatures and in the presence of a strong magnetic field, these systems exhibit fascinating, often unexpected, many-body states, arising from the strong electron-electron interaction. In our work, we studied various many-body states of different 2D systems. These included 2D electron and hole systems confined to GaAs and also to AlAs quantum wells, including wide quantum wells where the charge distribution is bilayer like. We observed and reported new phenomena in these systems, including new (even-denominator) fractional quantum Hall states, Wigner crystal solid phases, and composite fermion compressible states.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Crystallization of polarons through charge and spin ordering transitions in 1T-TaS 2

The interaction of electrons with the lattice in metals can lead to reduction of their kinetic energy to the point where they may form heavy, dressed quasiparticles—polarons. Unfortunately, polaronic lattice distortions are difficult to distinguish from more conventional charge- and spin-ordering phenomena at low temperatures. Here we present a study of local symmetry breaking of the lattice structure on the picosecond timescale in the prototype layered dichalcogenide Mott insulator 1T-TaS 2 using X-ray pair-distribution function measurements. We clearly identify symmetry-breaking polaronic lattice distortions at temperatures well above the ordered phases, and record the evolution of broken symmetry states from 915 K to 15 K. The data imply that charge ordering is driven by polaron crystallization into a Wigner crystal-like state, rather than Fermi surface nesting or conventional electron-phonon coupling. At intermediate temperatures the local lattice distortions are found to be consistent with a quantum spin liquid state.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Electronic rotons and Wigner crystallites in a two-dimensional dipole liquid

A key concept proposed by Landau to explain superfluid liquid helium is the elementary excitation of quantum particles called rotons1–8. The irregular arrangement of atoms in a liquid leads to the aperiodic dispersion of rotons, which played a pivotal role in understanding fractional quantum Hall liquids (magneto-rotons)9,10 and the supersolidity of Bose–Einstein condensates11–13. Even for a two-dimensional electron or dipole liquid, in the absence of a magnetic field, the repulsive interactions have been predicted to form a roton minimum14–19, which can be used to trace the transition to Wigner crystals20–24 and superconductivity25–27, although this has not yet been observed. Here, we report the observation of such electronic rotons in a two-dimensional dipole liquid of alkali-metal ions donating electrons to surface layers of black phosphorus. Our data reveal the striking aperiodic dispersion of rotons, which is characterized by a local minimum of energy at finite momentum. As the density of dipoles decreases so that interactions dominate over the kinetic energy, the roton gap reduces to 0, as in a crystal, signalling Wigner crystallization. Our model shows the importance of short-range order arising from repulsion between dipoles, which can be viewed as the formation of Wigner crystallites (bubbles or stripes) floating in the sea of a Fermi liquid. Our results reveal that the primary origin of electronic rotons (and the pseudogap) is strong correlations.

Park, Soobin↗
DOE OSTI2026

An exciton crystal in a moiré excitonic insulator

Strong Coulomb interactions can drive electrons to crystallize into a Wigner lattice. Achieving the bosonic analogue—a crystal of excitons—has remained challenging owing to their short lifetimes and weaker interactions. Here we report the observation of a thermodynamically stable exciton crystal in an excitonic insulator coupled to a moiré potential. Using an electron–hole bilayer composed of a monolayer MoSe 2 and a WS 2 /WSe 2 moiré superlattice, we constructed a tunable extended Bose–Hubbard system with electrical control over exciton and charge doping in thermal equilibrium. Optical spectroscopy revealed spontaneous crystallization of long-lived excitons at one exciton filling per three moiré sites, manifested as strong Umklapp scattering peaks. Exciton transport measurements further showed a pronounced exciton resistance peak at the same filling. When doped away from net charge neutrality, this moiré electron–hole bilayer can host correlated insulating phases in which dipolar excitonic insulators form on top of the background of a hole Mott insulator or generalized Wigner crystals. In conclusion, these findings establish moiré electron–hole bilayers as a versatile platform for realizing correlated crystalline phases of bosons and fermions.

Qi, Ruishi [University of California, Berkeley, CA↗
DOE OSTI2025

Imaging quantum melting in a disordered 2D Wigner solid

Two-dimensional strongly interacting electrons crystalize into a solid phase known as the Wigner crystal at low densities and form a Fermi liquid at high densities. At intermediate densities, the two-dimensional solid evolves into a strongly correlated liquid phase around a critical density. We observed this quantum melting of a disordered Wigner solid in bilayer molybdenum diselenide (MoSe2) using a noninvasive scanning tunneling microscopy imaging technique. At low densities, the Wigner solid forms nanocrystalline domains pinned by local disorder. It exhibits a quantum densification behavior with increased densities in the solid phase. Above a threshold density, the Wigner solid melts locally and enters a mixed phase in which solid and liquid regions coexist. The liquid regions expand and form a percolation network at even higher densities.

Xiang, Ziyu↗
DOE OSTI2025

Interplay of superconducting, metallic, and crystalline states of composite fermions at 𝜈 = $\frac{1}{6}$ in wide quantum wells

Evidence for developing fractional quantum Hall effect (FQHE) at filling fraction 𝜈 = 1/6 and 1/8 was recently reported in wide GaAs quantum wells [Wang et al., Phys. Rev. Lett. 134, 046502 (2025)]. In this article, we theoretically investigate the nature of the state at 𝜈 = 1/6 as a function of the quantum well width and the density by considering composite-fermion (CF) crystals, CF Fermi sea, and various kinds of paired CF states. The 𝑓-wave paired state has the lowest energy among the paired CF states. However, for parameters of interest, the energies of the CF crystal, the CF Fermi liquid, and the 𝑓-wave paired CF state are too close to distinguish. We, therefore, predict that 𝑖𝑓 the FQHE at 𝜈 = 1/6 is experimentally confirmed, this state would be an 𝑓-wave paired state of CFs, which can be verified by measurement of its thermal Hall conductance. Exact diagonalization studies on clean systems with up to eight electrons show that the ground states at 𝜈 = 𝑛/(6⁢𝑛 ± 1) are incompressible for all widths and densities we have considered, and are well described by the corresponding Laughlin and Jain states. We propose a phase diagram for large quantum well widths and densities in which at zero disorder, incompressible FQHE states are stabilized at 𝜈 = 𝑛/(6⁢𝑛 ± 1) and 𝜈 = 1/6, but in between these fillings the CF crystal is stabilized. We also present a qualitative discussion on the effects of disorder and propose a schematic phase diagram based on it. With disorder, which creates a spatial variation in the filling factor, two regimes are identified: (i) for small disorder, when the incompressible states percolate at the special fillings, FQHE with quantized Hall plateaus and vanishing longitudinal resistance should occur; and (ii) for larger disorder, when the CF crystal percolates, the longitudinal resistance rises with decreasing temperature but the domains of FQHE liquid produce minima at the special filling factors. Here, experiments are consistent with the latter scenario. We also mention a possible connection of the phase diagram presented here to a puzzling behavior observed for the fractional quantum anomalous Hall effect in pentalayer graphene.

Composite fermions↗
DOE OSTI2022

Correlated States of 2D Electrons near the Landau Level Filling ν = 1 / 7

The ground state of two-dimensional electron systems (2DESs) at low Landau level filling factors ( ν ≲ 1 / 6 ) has long been a topic of interest and controversy in condensed matter. Following the recent breakthrough in the quality of ultrahigh-mobility GaAs 2DESs, we revisit this problem experimentally and investigate the impact of reduced disorder. In a GaAs 2DES sample with density n = 6.1 × 10 10 / cm 2 and mobility μ = 25 × 10 6 cm 2 / V s , we find a deep minimum in the longitudinal magnetoresistance ( R x x ) at ν = 1 / 7 when T ≃ 104 mK . There is also a clear sign of a developing minimum in R x x at ν = 2 / 13 . While insulating phases are still predominant when ν ≲ 1 / 6 , these minima strongly suggest the existence of fractional quantum Hall states at filling factors that comply with the Jain sequence ν = p / ( 2 m p ± 1 ) even in the very low Landau level filling limit. The magnetic-field-dependent activation energies deduced from the relation R x x ∝ e E A / 2 k T corroborate this view and imply the presence of pinned Wigner solid states when ν ≠ p / ( 2 m p ± 1 ) . Similar results are seen in another sample with a lower density, further generalizing our observations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Anisotropic Two-Dimensional Disordered Wigner Solid

The interplay between the Fermi sea anisotropy, electron-electron interaction, and localization phenomena can give rise to exotic many-body phases. An exciting example is an anisotropic two-dimensional (2D) Wigner solid (WS), where electrons form an ordered array with an anisotropic lattice structure. Such a state has eluded experiments up to now as its realization is extremely demanding: First, a WS entails very low densities where the Coulomb interaction dominates over the kinetic (Fermi) energy. Attaining such low densities while keeping the disorder low is very challenging. Second, the low-density requirement has to be fulfilled in a material that hosts an anisotropic Fermi sea. Here, we report transport measurements in a clean (low-disorder) 2D electron system with anisotropic effective mass and Fermi sea. The data reveal that at extremely low electron densities, when the r s parameter, the ratio of the Coulomb to the Fermi energy, exceeds ≃ 38, the current-voltage characteristics become strongly nonlinear at small dc biases. Several key features of the nonlinear characteristics, including their anisotropic voltage thresholds, are consistent with the formation of a disordered, anisotropic WS pinned by the ubiquitous disorder potential.

42 ENGINEERING↗
DOE OSTI2021

Integration of a Wigner effect-based energy storage system with an advanced nuclear reactor

In this work, an innovative energy storage concept based on the purposeful creation of defects in crystalline material by neutron irradiation is presented. Lattice defects are generated when heavy particles collide with the atoms in a crystal structure, i.e., if the incoming particles have enough energy, recoil atoms are displaced from their initial lattice sites. Most of the displaced atoms will eventually combine with nearby vacancies, but some of them will come to rest in non-ideal locations. The energy held by displaced atoms is called Wigner energy. Lattice defects can migrate and form clusters, and the Wigner energy can be released from these groupings if sufficient activation energy is provided. In the nuclear industry, this effect is well-known since it represented an issue for graphite-moderated reactors. This work presents the conceptual design of an engineering system that exploits this physical process to store the energy of neutrons in advanced reactor concepts. In the first part of the paper, the theoretical performance of an energy storage system based on the Wigner effect is described. Given the lattice properties and the compatibility with the harsh reactor environment, graphite was selected as the candidate material for the irradiation targets. Both experimental data and molecular dynamics simulations confirmed that this system can achieve performance comparable with state-of-the-art batteries in terms of stored energy density. In the second part of the paper, the engineering challenges of this innovative technology and the proposed solutions are described. After defining the optimal irradiation conditions, the different steps of the operation of the proposed energy system (from energy storing to energy harvesting) were defined. Finally, the integration of this concept with advanced reactor designs, i.e., a Sodium-cooled Fast Reactor and a Molten Salt-cooled Reactor, was investigated and the corresponding performance was evaluated.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

Candidate structure for the H 2 -PRE phase of solid hydrogen

Experimental progress finally reached the metallic solid hydrogen phase, which was predicted by Wigner and Huntington over 80 years ago. However, the different structures in the phase diagram are still being debated due to the difficulty of diffraction experiments for high-pressured hydrogen. The determination of crystal structures under extreme condition is both of the basic condensed matter physics, and in planetary science: the behavior of giant gaseous planets (e.g., Jupiter and Saturn) strongly depends on the properties of inner high-pressured hydrogen. This work describes possible structures appearing under high pressures of 400~600 GPa. We applied a structural search using particle swarm optimization with density functional theory (DFT) to propose several candidate structures. For these structures, we performed fixed-node diffusion Monte Carlo simulations combined with DFT zero-point energy corrections to confirm their relative stability. We found P2 1 /c-8 as a promising candidate structure for the H 2 -PRE phase. P2 1 /c-8 is predicted the most stable at 400 and 500 GPa. P2 1 /c-8 reproduces qualitatively the IR spectrum peaks observed in the H 2 -PRE phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Distorted dislocation cores and asymmetric glide resistances in titanium

The determination of Critical Resolved Shear Stress (CRSS) in titanium for basal, prismatic, and pyramidal slip-planes without empirical constants is presented by combining Density Functional Theory (DFT) and anisotropic elasticity. A new mechanism leading to tension-compression (T-C) asymmetry in the CRSS levels has been revealed for the first time. The conditions for this asymmetry are established, involving a complex interplay between the dislocation core-structure and core-advance behavior. The three conditions for T-C asymmetry that need to be simultaneously satisfied can be summarized as: (1) a medium stacking fault width, d, (3 < d/b F < 10, where b F is the magnitude of the Burgers vector of the full dislocation), (2) an asymmetric core-structure of the extended dislocation (ξ 1 ≠ ξ 2 , where ξ 1 and ξ 2 are the core-widths of the first and second partials, respectively), and (3) intermittent motion of the partials (Δd/b F ≠ 0, where Δd is the magnitude of fluctuation in stacking fault width during intermittent motion). Pyramidal-slip in titanium satisfies all three conditions, resulting in significant T-C asymmetry. The CRSS theory considers a Wigner-Seitz (W-S) cell based domain area assigned to each lattice site for the calculations of core-energies accurately capturing the slip-plane lattice. The W-S based approach is essential due to the lower symmetry of the HCP crystal circumventing potential errors associated with the one-dimensional atomic-row approximation. Dislocation core structures are obtained for all the slip-systems in titanium showing significant distortion of the disregistry profile governing the core-advance behavior. The CRSS values predicted from the theory show agreement with the experimental CRSS levels reported in the literature.

Dislocation core↗