Search NASA⌕ Search

SEARCH · Search NASA

Results for “valley symmetry”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Weak-Field Hall Resistivity and Spin-Valley Flavor Symmetry Breaking in Magic-Angle Twisted Bilayer Graphene

Near a magic twist angle, the lowest energy conduction and valence bands of bilayer graphene moiré superlattices become extremely narrow. The band dispersion that remains is sensitive to the moiré’s strain pattern, nonlocal tunneling between layers, and filling-factor-dependent Hartree and exchange band renormalizations. In this Letter, we analyze the influence of these band-structure details on the pattern of flavor symmetry breaking observed in this narrow band system and on the associated pattern of Fermi surface reconstructions revealed by weak-field Hall and Shubnikov–de Haas magnetotransport measurements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Visualizing broken symmetry and topological defects in a quantum Hall ferromagnet

The interaction between electrons in graphene under high magnetic fields drives the formation of a rich set of quantum Hall ferromagnetic (QHFM) phases with broken spin or valley symmetry. Visualizing atomic-scale electronic wave functions with scanning tunneling spectroscopy (STS), we resolved microscopic signatures of valley ordering in QHFM phases and spectral features of fractional quantum Hall phases of graphene. At charge neutrality, we observed a field-tuned continuous quantum phase transition from a valley-polarized state to an intervalley coherent state, with a Kekulé distortion of its electronic density. Mapping the valley texture extracted from STS measurements of the Kekulé phase, we could visualize valley skyrmion excitations localized near charged defects. Our techniques can be applied to examine valley-ordered phases and their topological excitations in a wide range of materials.

valley symmetry↗
DOE OSTI2021

Twisted symmetric trilayer graphene: Single-particle and many-body Hamiltonians and hidden nonlocal symmetries of trilayer moiré systems with and without displacement field

Here, we derive the Hamiltonian for trilayer moiré systems with the Coulomb interaction projected onto the bands near the charge neutrality point. Motivated by the latest experimental results, we focus on the twisted symmetric trilayer graphene (TSTG) with a mirror symmetry with respect to the middle layer. We provide a full symmetry analysis of the noninteracting Hamiltonian with a perpendicular displacement field coupling the band structure made otherwise of the twisted bilayer graphene (TBG) and the high-velocity Dirac fermions, and we identify a hidden nonlocal symmetry of the problem. In the presence of this displacement field, we construct an approximate single-particle model, akin to the tripod model for TBG, capturing the essence of noninteracting TSTG. We also derive more quantitative perturbation schemes for the low-energy physics of TSTG with displacement field, obtaining the corresponding eigenstates. This allows us to obtain the Coulomb interaction Hamiltonian projected in the active band TSTG wave functions and derive the full many-body Hamiltonian of the system. We also provide an efficient parametrization of the interacting Hamiltonian. Finally, we show that the discrete symmetries at the single-particle level promote the U (2) × U (2) spin-valley symmetry to enlarged symmetry groups of the interacting problem under different limits. The interacting part of the Hamiltonian exhibits a large U (4) × U (4) × U (4) × U (4) symmetry in the chiral limit. Moreover, by identifying a symmetry which we dub spatial many-body charge conjugation, we show that the physics of TSTG is symmetric around charge neutrality.

2-dimensional systems↗
DOE OSTI2022

Spontaneous time-reversal symmetry breaking in twisted double bilayer graphene

Twisted double bilayer graphene (tDBG) comprises two Bernal-stacked bilayer graphene sheets with a twist between them. Gate voltages applied to top and back gates of a tDBG device tune both the flatness and topology of the electronic bands, enabling an unusual level of experimental control. Metallic states with broken spin and valley symmetries have been observed in tDBG devices with twist angles in the range 1.2–1.3°, but the topologies and order parameters of these states have remained unclear. We report the observation of an anomalous Hall effect in the correlated metal state of tDBG, with hysteresis loops spanning hundreds of mT in out-of-plane magnetic field (B ⊥ ) that demonstrate spontaneously broken time-reversal symmetry. The B ⊥ hysteresis persists for in-plane fields up to several Tesla, suggesting valley (orbital) ferromagnetism. At the same time, the resistivity is strongly affected by even mT-scale values of in-plane magnetic field, pointing to spin-valley coupling or to a direct orbital coupling between in-plane field and the valley degree of freedom.

36 MATERIALS SCIENCE↗
DOE OSTI2022

SU(4) Symmetry in Twisted Bilayer Graphene: An Itinerant Perspective

We study symmetry-broken phases in twisted bilayer graphene at small filling above charge neutrality and at van Hove filling. We argue that the Landau functionals for the particle-hole order parameters at these fillings both have an approximate SU(4) symmetry, but differ in the sign of quartic terms. We determine the order parameter manifold of the ground state and analyze its excitations. For small fillings, we find a strong first-order transition to an SU(3) Ⓧ U(1) manifold of orders that break spin-valley symmetry and induce a 3-1 splitting of fermionic excitations. For van Hove filling, we find a weak first-order transition to an SU(2) Ⓧ SU(2) Ⓧ U(1) manifold of orders that preserves the twofold band degeneracy. Here, we discuss the effect of particle-hole orders on superconductivity and compare with strong-coupling approaches.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Site-controlled telecom-wavelength single-photon emitters in atomically-thin MoTe2

Abstract Quantum emitters (QEs) in two-dimensional transition metal dichalcogenides (2D TMDCs) have advanced to the forefront of quantum communication and transduction research. To date, QEs capable of operating in O-C telecommunication bands have not been demonstrated in TMDCs. Here we report site-controlled creation of telecom QEs emitting over the 1080 to 1550 nm telecommunication wavelength range via coupling of 2D molybdenum ditelluride (MoTe 2 ) to strain inducing nano-pillar arrays. Hanbury Brown and Twiss experiments conducted at 10 K reveal clear photon antibunching with 90% single-photon purity. The photon antibunching can be observed up to liquid nitrogen temperature (77 K). Polarization analysis further reveals that while some QEs display cross-linearly polarized doublets with ~1 meV splitting resulting from the strain induced anisotropic exchange interaction, valley degeneracy is preserved in other QEs. Valley Zeeman splitting as well as restoring of valley symmetry in cross-polarized doublets are observed under 8 T magnetic field.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Nature of the Correlated Insulator States in Twisted Bilayer Graphene

We use self-consistent Hartree-Fock calculations performed in the full $\pi$-band Hilbert space to assess the nature of the recently discovered correlated insulator states in magic-angle twisted bilayer graphene (TBG). In this work, we find that gaps between the flat conduction and valence bands open at neutrality over a wide range of twist angles, sometimes without breaking the system’s valley projected $\mathcal{C}_2\mathcal{T}$ symmetry. Broken spin-valley flavor symmetries then enable gapped states to form not only at neutrality, but also at total moiré band filling $\textit{n}$ = ± $\textit{p}/4$ with integer $\textit{p}$ = 1, 2, 3, when the twist angle is close to the magic value at which the flat bands are most narrow. Because the magic-angle flat band quasiparticles are isolated from remote band quasiparticles only for effective dielectric constants larger than ~20, the gapped states do not necessarily break $\mathcal{C}_2\mathcal{T}$ symmetry and as a consequence the insulating states at $\textit{n}$ = ± 1/ 4 and $\textit{n}$ = ± 3/4 need not exhibit a quantized anomalous Hall effect.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Spin and orbital metallic magnetism in rhombohedral trilayer graphene

We provide a theoretical interpretation of the metallic broken spin-valley (flavor) symmetry states recently discovered in hole-doped rhombohedral trilayer (ABC) graphene in large electric displacement fields. Our conclusions about the phase diagram and phase transitions combine insights from ABC graphene electronic structure models and mean-field theory, and are guided by the precise magneto-oscillation Fermi-surface-area measurements of recent experiments. We find that the principle of momentum-space condensation plays a key role in determining Fermi-surface reconstructions enabled by broken flavor symmetries when the single-particle bands imply thin annular Fermi seas. The reconstructed Fermi sea consists of one large outer Fermi-surface-enclosed majority-flavor states in reciprocal-space area A maj and one or more small inner holelike Fermi-surface-enclosed minority-flavor states in A min that are primarily responsible for nematic order. The competing ground states (valley-Ising, valley-XY, and spin-polarized state) have different A maj /A min and exchange energy maximizes this ratio and selects valley-XY nematic metal as the lowest-energy state. Here, we discuss how the nematic pockets explain the observed fractionalization of quantum oscillation frequencies, and propose anisotropic transport and the nonlinear Hall effect as additional observables.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Spin-triplet superconductivity from intervalley Goldstone modes in magic-angle graphene

Here, we consider magic-angle graphene in the doping regime around charge neutrality, and we study the connection between a recently proposed intervalley coherent insulator at zero doping and the neighboring superconducting domes. The magic-angle graphene continuum model has an emergent U(1) valley-charge conservation symmetry and an emergent SU(2) symmetry corresponding to opposite spin rotations in the two valleys. The intervalley coherent insulator spontaneously breaks both these emergent symmetries, and as a result has four Goldstone modes that couple to doped charge carriers. We derive the effective interaction mediated by the Goldstone modes, and we study its role in electron pair formation. The SU(2) Goldstone modes generate a ferromagnetic interaction, which is attractive in spin-triplet pairing channels and repulsive in spin-singlet channels. From a weak-coupling BCS calculation, we find the leading superconducting instability in the p-wave channel.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Phase diagram of twisted bilayer graphene at filling factor $v = ±3$

Here, we study the correlated insulating phases of twisted bilayer graphene (TBG) in the absence of lattice strain at integer filling $v = ±3$. Using the self-consistent Hartree-Fock method on a particle-hole symmetric model and allowing translation symmetry breaking terms, we obtain the phase diagram with respect to the ratio of AA interlayer hopping (w 0 ) and AB interlayer hopping (w 1 ). When the interlayer hopping ratio is close to the chiral limit (w 0 /w 1 ≲ 0.5), a quantum anomalous Hall state with Chern number v c = ±1 can be observed consistent with previous studies. Around the realistic value w 0 /w 1 ≈ 0.8, we find a spin and valley polarized, translation symmetry breaking, state with C 2⁢z T symmetry, a charge gap and a doubling of the moiré unit cell, dubbed theC 2⁢z T stripe phase. The real-space total charge distribution of this C 2⁢z T stripe phase in the flat band limit does not have modulation between different moiré unit cells, although the charge density in each layer is modulated, and the translation symmetry is strongly broken. Other symmetries, including C 2⁢z , C 2⁢x , particle-hole symmetry P, and the topology of the C 2⁢z T stripe phase, are also discussed in detail. We observed braiding and annihilation of the Dirac nodes by continuously turning on the order parameter to its fully self-consistent value, and provide a detailed explanation of the mechanism for the charge gap opening despite preserving C 2⁢z T and valley U⁡(1) symmetries. In the transition region between the quantum anomalous Hall phase and the C 2⁢z T stripe phase, we find an additional competing state with comparable energy corresponding to a phase with a tripling of the moiré unit cell.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Polaritonic Chern Insulators in Monolayer Semiconductors

Systems with strong light-matter interaction open up new avenues for studying topological phases of matter. Examples include exciton polaritons, mixed light-matter quasiparticles, where the topology of the polaritonic band structure arises from the collective coupling between matter wave and optical fields strongly confined in periodic dielectric structures. Distinct from light-matter interaction in a uniform environment, the spatially varying nature of the optical fields leads to a fundamental modification of the well-known optical selection rules, which were derived under the plane wave approximation. Here, in this study, we identify polaritonic Chern insulators by coupling valley excitons in transition metal dichalcogenides to photonic Bloch modes in a dielectric photonic crystal slab. We show that polaritonic Dirac points, which are markers for topological phase transition points, can be constructed from the collective coupling between valley excitons and photonic Dirac cones in the presence of both time-reversal and inversion symmetries. Lifting exciton valley degeneracy by breaking time-reversal symmetry leads to gapped polaritonic bands with nonzero Chern numbers. Through numerical simulations, we predict polaritonic chiral edge states residing inside the topological gaps. Our Letter paves the way for the further study of strong exciton-photon interaction in nanophotonic structures and for exploring polaritonic topological phases and their practical applications in polaritonic devices.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Interaction effects in graphene in a weak magnetic field

A weak perpendicular magnetic field, B, breaks the chiral symmetry of each valley in the electron spectrum of graphene, preserving the overall chiral symmetry in the Brillouin zone. Here we explore the consequences of this symmetry breaking for the interaction effects in graphene. In particular, we demonstrate that the electron-electron interaction lifetime acquires an anomalous B dependence. Also, the ballistic zero-bias anomaly, δv(ω), where ω is the energy measured from the Fermi level, emerges at a weak B and has the form δv(B) ~ B 2 /ω 2 . Temperature dependence of the magnetic-field corrections to the thermodynamic characteristics of graphene is also anomalous. We discuss experimental manifestations of the effects predicted. The microscopic origin of the B-field sensitivity is an extra phase acquired by the electron wave function resulting from the chirality-induced pseudospin precession.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Magnetism in Moiré Materials

This project focused on the theory of the electronic properties of magnetic moire materials. Moire materials can be formed by overlaying two or more two-dimensional crystals that are either semiconductors or semimetals and establishing a moire pattern. Low-energy electronic properties are then described by a continuum model with crystalline periodicity. Moire materials are therefore artificial two-dimensional crys- tals whose periodicity is at the tens of nanometers scale, increasing the unit cell area by a factor of about 10,000 compared to real crystals. They are important because the main tuning knob of chemistry, the number of electrons per effective atom or molecule (the analog of the number of electrons per unit cell in real crystals), can be shifted by more than one simply by using electrical gates. The research covered two diffeerent classes of moire materials, graphene multilayers twisted to a rotation angle at which correlations are strong, and transition metal dichalcogenide semiconductors. The proposal identifed one project in each area both related very broadly to magnetism: i) Advancing understanding of broken spin-valley and sublattice symmetries in Magic Angle Twisted Bilayer Graphene and ii) Developing the theory of itinerant electron magnetism in Gamma-valley and K-valley transition metal dichalcogenide moire materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Superconductivity in a doped valley coherent insulator in magic angle graphene: Goldstone-mediated pairing and Kohn-Luttinger mechanism

We consider magic angle graphene in the doping regime around charge neutrality and study the connection between a recently proposed inter-valley coherent insulator at zero doping and the neighboring superconducting domes. The breaking of the valley U(1) symmetry leads to massless Goldstone modes, which couple to the doped charge carriers. We derive the effective interaction between these Goldstone modes and the conduction electrons and study its role in mediating superconductivity. Combining it with the screened Coulomb potential, we find weak-coupling superconducting instabilities in the two-component p- and d-wave channels. The competition between the two channels is set by the distance between the bilayer graphene device and the metallic gates. We find that the p-wave instability originates from the attraction mediated by the Goldstone modes, while the d-wave pairing is caused purely by the screened Coulomb interaction, similarly to the Kohn-Luttinger mechanism.

Kozii, Vladyslav↗
DOE OSTI2020

A chiral switchable photovoltaic ferroelectric 1D perovskite

Spin and valley degrees of freedom in materials without inversion symmetry promise previously unknown device functionalities, such as spin-valleytronics. Control of material symmetry with electric fields (ferroelectricity), while breaking additional symmetries, including mirror symmetry, could yield phenomena where chirality, spin, valley, and crystal potential are strongly coupled. Here we report the synthesis of a halide perovskite semiconductor that is simultaneously photoferroelectricity switchable and chiral. Spectroscopic and structural analysis, and first-principles calculations, determine the material to be a previously unknown low-dimensional hybrid perovskite (R)-(-)-1-cyclohexylethylammonium/(S)-(+)-1 cyclohexylethylammonium) PbI 3 . Optical and electrical measurements characterize its semiconducting, ferroelectric, switchable pyroelectricity and switchable photoferroelectric properties. Temperature dependent structural, dielectric and transport measurements reveal a ferroelectric-paraelectric phase transition. Circular dichroism spectroscopy confirms its chirality. The development of a material with such a combination of these properties will facilitate the exploration of phenomena such as electric field and chiral enantiomer–dependent Rashba-Dresselhaus splitting and circular photogalvanic effects

36 MATERIALS SCIENCE↗
DOE OSTI2020

Dirac-Harper Theory for One-Dimensional Moiré Superlattices

In this work, we study a Dirac-Harper model for moiré bilayer superlattices where layer antisymmetric strain periodically modulates the interlayer coupling between two honeycomb lattices in one spatial dimension. Discrete and continuum formulations of this model are analyzed. For a sufficiently long moiré period we find low-energy spectra that host a manifold of weakly dispersive bands arising from a hierarchy of momentum and position-dependent mass inversions. We analyze their charge distributions, mode count, and valley coherence using exact symmetries of the lattice model and approximate symmetries of a four-flavor version of the Jackiw-Rebbi one-dimensional solution.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Valley-spin polarization at zero magnetic field induced by strong hole-hole interactions in monolayer WSe 2

Monolayer transition metal dichalcogenides have emerged as prominent candidates to explore the complex interplay between spin and valley degrees of freedom. Their strong spin-orbit interaction and broken inversion symmetry lead to the spin-valley locking effect, in which carriers occupying theKandK′ valleys of the reciprocal space must have opposite spins. This effect is particularly strong for holes due to a larger spin-orbit gap in the valence band. By reducing the dimensionality of a monolayer of WSe 2 to 1D via electrostatic confinement, we demonstrate that spin-valley locking and strong hole-hole interactions lead to a ferromagnetic state where hole transport is spin-valley polarized, even without an applied magnetic field. A massive Dirac fermion model in the Hartree-Fock approximation reveals that many-body hole-exchange interactions lead to this polarized ground-state. This observation opens the possibility of implementing a robust and stable valley-polarized system, essential in valleytronic applications.

Science & Technology - Other Topics↗
DOE OSTI2021

Topological and nematic superconductivity mediated by ferro-SU(4) fluctuations in twisted bilayer graphene

We propose an SU(4) spin-valley-fermion model to investigate the superconducting instabilities of twisted bilayer graphene (TBG). In this approach, bosonic fluctuations associated with an emergent SU(4) symmetry, corresponding to combined rotations in valley and spin spaces, couple to the low-energy fermions that comprise the flat bands. These fluctuations are peaked at zero wave vector, reflecting the “ferromagnetic-like” SU(4) ground state recently found in strong-coupling solutions of microscopic models for TBG. Focusing on electronic states related to symmetry-imposed points of the Fermi surface, dubbed here “valley hot-spots” and “van Hove hot-spots,” we find that the coupling to the itinerant electrons partially lifts the huge degeneracy of the ferro-SU(4) ground state manifold, favoring intervalley order, spin-valley coupled order, ferromagnetic order, spin-current order, and valley-polarized order, depending on details of the band structure. Here, these fluctuations, in turn, promote attractive pairing interactions in a variety of closely competing channels, including a nodeless f-wave state, a nodal i-wave state, and topological d+id and p+ip states with unusual Chern numbers 2 and 4, respectively. Nematic superconductivity, although not realized as a primary instability of the system, appears as a consequence of the near-degeneracy of superconducting order parameters that transform as one-dimensional and two-dimensional irreducible representations of the point group D 6 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗