Electron fractionalization in two-dimensional graphenelike structures

Abstract

Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall fluids, where time-reversal symmetry is broken by a large external magnetic field. Recently, there has been a tremendous effort in the search for examples of fractionalization in two-dimensional systems with time-reversal symmetry. In this letter, we show that fractionally charged topological excitations exist on graphenelike structures, where quasiparticles are described by two flavors of Dirac fermions and time-reversal symmetry is respected. The topological zero-modes are mathematically similar to fractional vortices in p-wave superconductors. They correspond to a twist in the phase in the mass of the Dirac fermions, akin to cosmic strings in particle physics.

4 pages, 2 figures

References in corpus (3)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Zero modes of tight binding electrons on the honeycomb lattice

Cited by in corpus (328)

• The electronic properties of graphene
• Electron-Electron Interactions in Graphene: Current Status and Perspectives
• Dirac materials
• Topological insulator on the kagome lattice
• Topological confinement in bilayer graphene
• Artificial graphene as a tunable Dirac material
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Topological photonic crystals: physics, designs and applications
• Theory of interacting electrons on the honeycomb lattice
• Exciton condensation and charge fractionalization in a topological insulator film
• Domain walls in gapped graphene
• Fractional excitations in the square-lattice quantum antiferromagnet
• Interaction-driven topological insulators on the kagome and the decorated honeycomb lattices
• Chiral d-wave superconductivity in doped graphene
• Dirac-vortex topological cavity
• Masses in graphene-like two-dimensional electronic systems: topological defects in order parameters and their fractional exchange statistics
• Chiral Gauge Theory for Graphene
• Dirac-point engineering and topological phase transitions in honeycomb optical lattices
• Charged Skyrmions and Topological Origin of Superconductivity in Magic Angle Graphene
• Fractional topological liquids with time-reversal symmetry and their lattice realization
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Magnetic-Moment Fragmentation and Monopole Crystallization
• Kekulé valence bond order in an extended Hubbard model on the honeycomb lattice, with possible applications to twisted bilayer graphene
• Pseudospins and topological effects of phonons in a Kekule lattice
• Chiral Topological Insulators, Superconductors and other competing orders in three dimensions
• Interaction driven instabilities of a Dirac semi-metal
• Unconventional superconductivity on honeycomb lattice: the theory of Kekule order parameter
• Topological kink states at a tilt boundary in gated multi-layer graphene
• Experimental evidence of chiral symmetry breaking in Kekulé-ordered graphene
• Topological one-way fiber of second Chern number
• Topological and geometrical aspects of band theory
• Fermion-induced quantum critical points
• Field-induced Kosterlitz-Thouless transition in the N=0 Landau level of graphene
• Spin Charge Separation in the Quantum Spin Hall State
• Topological Properties of Electrons in Honeycomb Lattice with Kekulé Hopping Textures
• Majorana Modes in Driven-Dissipative Atomic Superfluids With Zero Chern Number
• Braiding photonic topological zero modes
• Majorana-like zero modes in Kekulé distorted sonic lattices
• Electronic multicriticality in bilayer graphene
• Electron fractionalization for two-dimensional Dirac fermions
• Quantizing Majorana Fermions in a Superconductor
• Quantum superconducting criticality in graphene and topological insulators
• Imaging tunable quantum Hall broken-symmetry orders in graphene
• Valley-momentum locking in a graphene superlattice with Y-shaped Kekulé bond texture
• Non-Abelian braiding of light
• Phases of correlated spinless fermions on the honeycomb lattice
• Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
• Electronic properties of graphene with a topological defect
• Valley engineering by strain in Kekulé-distorted graphene
• Charge instabilities and topological phases in the extended Hubbard model on the honeycomb lattice with enlarged unit cell
• Energy gap opening in submonolayer lithium on graphene: Local density functional and tight-binding calculations
• Band gap opening by two-dimensional manifestation of Peierls instability in graphene
• Topological phase transitions in the non-Abelian honeycomb lattice
• Topological Insulators on the Decorated Honeycomb Lattice
• STM Study of Quantum Hall Isospin Ferromagnetic States of Zero Landau Level in Graphene Monolayer
• Parent Hamiltonian for the Chiral Spin Liquid
• Interaction driven phases in the half-filled honeycomb lattice: an infinite density matrix renormalization group study
• Dimerized Solids and Resonating Plaquette Order in SU(N)-Dirac Fermions
• Mirror winding number and helical edge modes in honeycomb lattice with hopping-energy texture
• Anomalous Spin Correlations and Mass-Generating Excitonic Instability of Interacting Weyl Fermions
• Interaction driven phases in the honeycomb lattice from exact diagonalization
• Irrational vs. rational charge and statistics in two-dimensional quantum systems
• Materials design from non-equilibrium steady states: driven graphene as a tunable semiconductor with topological properties
• Fractionally charged topological point defects on the kagome lattice
• Kekule' textures, pseudo-spin one Dirac cones and quadratic band crossings in a graphene-hexagonal indium chalcogenide bilayer
• Induced fermionic current in toroidally compactified spacetimes with applications to cylindrical and toroidal nanotubes
• Bound States of Conical Singularities in Graphene-Based Topological Insulators
• Ising and Gross-Neveu model in next-to-leading order
• Massless Dirac Fermions in a Square Optical Lattice
• Dirac-vortex topological photonic crystal fibre
• Deconfined fractional electric charges in graphene at high magnetic fields
• A Photonic Topological Mode Bound to a Vortex
• Geometrical and topological aspects of graphene and related materials
• Fermion-induced quantum criticality in two-dimensional Dirac semimetals: Non-perturbative flow equations, fixed points and critical exponents
• Fractionalization in a square-lattice model with time-reversal symmetry
• Effective Model for Fractional Topological Corner Modes in Quasicrystals
• Poor man's topological quantum gate based on the Su-Schrieffer-Heeger model
• Fractional Fermions with Non-Abelian Statistics
• Room-temperature continuous-wave Dirac-vortex topological lasers on silicon
• Anyons in a weakly interacting system
• Topological Fermi liquids from Coulomb interactions in the doped Honeycomb lattice
• Fermionic condensate and Casimir densities in the presence of compact dimensions with applications to nanotubes
• Manifestations of topological effects in graphene
• Near zero modes in condensate phases of the Dirac theory on the honeycomb lattice
• Gauge-field-assisted Kekulé quantum criticality
• Edge-dependent topology in Kekulé lattices
• Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice
• Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
• Topological insulator in the core of the superconducting vortex in graphene
• Intertwining of magnetism and charge ordering in kagome FeGe
• Anderson localization and the topology of classifying spaces
• Vortices, zero modes and fractionalization in bilayer-graphene exciton condensate
• Isospin of topological defects in Dirac systems
• Qsymm: Algorithmic symmetry finding and symmetric Hamiltonian generation
• Fermi velocity renormalization and dynamical gap generation in graphene
• Ground-state properties of gapped graphene using the random phase approximation
• Topological Edge States and Fractional Quantum Hall Effect from Umklapp Scattering
• Zero-energy states and fragmentation of spin in the easy-plane antiferromagnet on a honeycomb lattice
• Pedestrian index theorem a la Aharonov-Casher for bulk threshold modes in corrugated multilayer graphene
• Absence of dynamical gap generation in suspended graphene
• Extended Hubbard model in undoped and doped monolayer and bilayer graphene: Selection rules and organizing principle among competing orders
• Double Weyl points and Fermi arcs of topological semimetals in non-Abelian gauge potentials
• Fermion-induced quantum criticality with two length scales in Dirac systems
• Non-Abelian braiding of Dirac fermionic modes using topological corner states in higher-order topological insulator
• Entanglement Hamiltonians for chiral fermions with zero modes
• Competing states in the SU(3) Heisenberg model on the honeycomb lattice: Plaquette valence-bond crystal versus dimerized color-ordered state
• Quantum Hall resistances of multiterminal top-gated graphene device
• Floquet systems coupled to particle reservoirs
• Exact Zero Modes in Closed Systems of Interacting Fermions
• Optimal traps in graphene
• Fractional charge bound to a vortex in two dimensional topological crystalline insulators
• Higher-Order Topological Phase in a Honeycomb-Lattice Model with Anti-Kekulé Distortion
• Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization
• Bulk-Defect Correspondence in Particle-Hole Symmetric Insulators and Semimetals
• Triggering a global density wave instability in graphene via local symmetry-breaking
• Lattice gauge theory model for graphene
• Fractional statistics of topological defects in graphene and related structures
• Fractional boundary charges in quantum dot arrays with density modulation
• The quantum valley Hall effect in proximity-induced superconducting graphene: an experimental window for deconfined quantum criticality
• Symmetry analysis of translational symmetry broken density waves: application to hexagonal lattices in two dimensions
• Corner states of topological fullerenes
• Lattice quantum electrodynamics for graphene
• Fermion-induced quantum critical points in two-dimensional Dirac semimetals
• Dynamical Floquet spectrum of Kekulé-distorted graphene under normal incidence of electromagnetic radiation
• Instabilities on graphene's honeycomb lattice with electron-phonon interactions
• Quantum phase transitions in Dirac fermion systems
• Observation of 2D Weyl Fermion States in Epitaxial Bismuthene
• Possible Lattice Distortions in the Hubbard Model for Graphene
• Effect of short-range interactions on the quantum critical behavior of spinless fermions on the honeycomb lattice
• The fate of interaction-driven topological insulators under disorder
• Fermionic current from topology and boundaries with applications to higher-dimensional models and nanophysics
• Determination of tunneling charge via current measurements
• Topological Invariant and Quantum Spin Models from Magnetic π Fluxes in Correlated Topological Insulators
• Resonant transport in Kekule-distorted graphene nanoribbons
• Quantum phase transition and fractional excitations in a topological insulator thin film with Zeeman and excitonic masses
• Unconventional pairing and electronic dimerization instabilities in the doped Kitaev-Heisenberg model
• Renormalization group aspects of graphene
• Ideal strength and phonon instability of strained monolayer materials
• Numerical evidence of conformal phase transition in graphene with long-range interactions
• Non-abelian gauge fields and quadratic band touchings in molecular graphene
• Heterostructures of graphene and topological insulators Bi${}_2$Se${}_3$, Bi${}_2$Te${}_3$, and Sb${}_2$Te${}_3$
• The effect of sublattice symmetry breaking on the electronic properties of a doped graphene
• Inducing topological order in a honeycomb lattice
• Symmetry breaking effects on spin and electronic transport in graphene
• Skyrmion zoo in graphene at charge neutrality in a strong magnetic field
• Zeeman-field-induced nontrivial topological phases in a one-dimensional spin-orbit-coupled dimerized lattice
• Bound States in Graphene
• Persistence of zero modes in a gauged Dirac model for bilayer graphene
• Persistence of chirality in the Su-Schrieffer-Heeger model in the presence of on-site disorder
• Zero-energy states bound to a magnetic pi-flux vortex in a two-dimensional topological insulator
• Distinct Competing Ordered ν=2 States in Bilayer Graphene
• Chalker scaling, level repulsion, and conformal invariance in critically delocalized quantum matter: Disordered topological superconductors and artificial graphene
• Coexistence of extended flat band and Kekulé order in Li-intercalated graphene
• Localized D-dimensional global k-defects
• Probing the topological properties of the Jackiw-Rebbi model with light
• Counting Majorana zero modes in superconductors
• Spontaneous breaking of Lorentz symmetry in $(2+\epsilon )$-dimensional QED
• Graphene with geometrically induced vorticity
• Classification of massive and gapless phases in bilayer graphene
• Vortex and gap generation in gauge models of graphene
• Irrational charge from topological order
• Interacting Dirac fermions under spatially alternating pseudo-magnetic field: Realization of spontaneous quantum Hall effect
• Excitonic and superconducting orders from repulsive interaction on the doped honeycomb bilayer
• 3/2 Fractional Quantum Hall Plateau in Confined Two-Dimensional Electron Gas
• Spin-Polarized Fractional Corner Charges and Their Photonic Realization
• Spin-Peierls instability of the U(1) Dirac spin liquid
• Asymmetric spatial structure of zero modes for birefringent Dirac fermions
• Zero modes and charged Skyrmions in graphene bilayer
• Comments on the Chern-Simons photon term in the QED description of graphene
• Fermionic Casimir densities in a conical space with a circular boundary and magnetic flux
• Symmetry-protected entangling boundary zero modes in crystalline topological insulators
• Observation of Kekulé vortices induced in graphene by hydrogen adatoms
• Quantum spin Hall effect and spin-charge separation in a kagome lattice
• Chiral Gauge Theory for Graphene Edge
• Phase diagram of interacting spinless fermions on the honeycomb lattice
• Annealing-induced long-range charge density wave order in magnetic kagome FeGe: fluctuations and disordered structure
• Simulation and measurement of the fractional particle number in one-dimensional optical lattices
• Tunable multiple layered Dirac cones in optical lattices
• Momentum dependence of quantum critical Dirac systems
• Dissipationless conductance in a topological coaxial cable
• Asymmetrically Doped Polyacetylene
• Charge confinement and Klein tunneling from doping graphene
• Topological nematic phase in Dirac semi-metals
• Disordered fermionic quantum critical points
• Zero-energy states of massive Dirac equation in magnetic fields
• Tailoring Dirac fermions by in-situ tunable high-order moire pattern in graphene-monolayer xenon heterostructure
• Masses and Majorana fermions in graphene
• Creation and manipulation of anyons in a layered superconductor-2DEG system
• A supersymmetric model for graphene
• Antilinear spectral symmetry and the vortex zero-modes in topological insulators and graphene
• Spectrum of the Dirac Hamiltonian with the mass-hedgehog in arbitrary dimension
• Magnetic field induced inequivalent vortex zero modes in strained graphene
• Dynamical fermion mass generation and exciton spectra in graphene
• Fermions in the presence of topological structures under geometric constrictions
• Vison crystals, chiral and crystalline phases in the Yao-Lee model
• Chern Insulators on Singular Geometries
• Absence of inhomogeneous chiral phases in 2+1-dimensional four-fermion and Yukawa models
• Time reversal, fermion doubling, and the masses of lattice Dirac fermions in three dimensions
• Dynamical Lorentz symmetry breaking in 3D and charge fractionalization
• Spontaneous Chiral Symmetry Breaking in Bilayer Graphene
• Lattice Field Theory Study of Magnetic Catalysis in Graphene
• Valence-Bond Order in a Honeycomb Antiferromagnet Coupled to Quantum Phonons
• Fermionic multicriticality near Kekulé valence-bond ordering in honeycomb lattice
• Valley-driven Zitterbewegung in Kekulé-distorted graphene
• BF-theory in graphene: a route toward topological quantum computing?
• Anyons in integer quantum Hall magnets
• Critical properties of the Néel/algebraic-spin-liquid transition
• Dynamic polarization and plasmons in kekulé-patterned graphene: Signatures of the broken valley degeneracy
• Second-order topological modes in two-dimensional continuous media
• Competing charge-density-wave, magnetic and topological ground states at and near Dirac points in graphene in axial magnetic fields
• Pairing symmetry and vortex zero-mode for superconducting Dirac fermions
• Torus Spectroscopy of the Gross-Neveu-Yukawa Quantum Field Theory: Free Dirac versus Chiral Ising Fixed Point
• Low energy electron-phonon effective action from symmetry analysis
• Global phase diagram of two-dimensional Dirac fermions in random potentials
• Light-modulated Josephson effect in Kekulé patterned graphene
• Fermion-induced quantum critical point in Dirac semimetals: a sign-problem-free quantum Monte Carlo study
• Topological Magnon Insulator with a Kekule Bond Modulation
• Kekule-distortion-induced Exciton instability in graphene
• Wilson-Fisher fixed points in presence of Dirac fermions
• Competition of First-Order and Second-Order Topology on the Honeycomb Lattice
• Geometric description of the Kitaev honeycomb lattice model
• Half-integer charge injection by a Josephson junction without excess noise
• Optoelectronic Fingerprints of Interference between Different Charge Carriers in Graphene Superlattices and Analogies to Twisted Graphene Bilayers
• Strain-induced excitonic instability in twisted bilayer graphene
• Hierarchical Majoranas in a Programmable Nanowire Network
• Midgap spectrum of the fermion-vortex system
• $Z_2$ index for gapless fermionic modes in the vortex core of three dimensional paired Dirac fermions
• Particle number fractionalization of a one-dimensional atomic Fermi gas with synthetic spin-orbit coupling
• Phase structure of monolayer graphene from effective U(1) gauge theory on honeycomb lattice
• Yang-Mills gauge theories from fermionic lattice models
• Topological gap states of semiconducting armchair graphene ribbons
• Kekulé Induced Valley Birefringence and Skew Scattering in Graphene
• Non-Abelian fermion parity interferometry of Majorana bound states in a Fermi sea
• Fullerenes, Zero-modes, and Self-adjoint Extensions
• Supersymmetric Runge-Lenz-Pauli vector for Dirac vortex in topological insulators and graphene
• Spontaneous mass generation due to phonons in a two-dimensional Dirac fermion system
• An amplitude-phase (Ermakov-Lewis) approach for the Jackiw-Pi model of bilayer graphene
• Deconfined criticality in bilayer graphene
• Quantum multicriticality of bilayer graphene in the presence of a tunable energy gap
• Competing orders in the Dirac-like electronic structure and the non-linear sigma model with the topological terms
• Uniaxial strain on gapped graphene
• Monopole topological resonators
• Realization of a vortex in the Kekule texture of molecular Graphene, at a Y junction where 3 domains meet
• Random-mass disorder in the critical Gross-Neveu-Yukawa models
• $\pi$-fluxes, semi-metals and flat bands in artificial materials
• Topological domain wall states in a non-symmorphic chiral chain
• Weyl Semimetal from the Honeycomb Array of Topological Insulator Nanowires
• Dyson-Schwinger approach to strongly coupled theories
• Dynamics of noisy quantum systems in the Heisenberg picture: application to the stability of fractional charge
• Competition of trivial and topological phases in patterned graphene based heterostructures
• Topological defects of Néel order and Kondo singlet formation for Kondo-Heisenberg model on a honeycomb lattice
• Relativistic Mott transitions and finite-temperature effects of quantum criticality in Dirac semimetals
• Lattice realization of the generalized chiral symmetry in two dimensions
• Topological effective field theories for Dirac fermions from index theorem
• Finite temperature fermion condensate, charge and current densities in a (2+1)-dimensional conical space
• A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields
• Skyrmion defects and competing singlet orders in a half-filled antiferromagnetic Kondo-Heisenberg model on the honeycomb lattice
• Effect of topological defects and Coulomb charge on the low energy quantum dynamics of gapped graphene
• Hierarchy of Spin and Valley Symmetry Breaking in Quantum Hall Single Layer Graphene
• Fractional Josephson effect in nonuniformly strained graphene
• Quasienergy spectra of a charged particle in planar honeycomb lattices
• Defects in Graphene : A Topological Description
• Edge states in a non-Hermitian topological crystalline insulator
• Translational symmetry breaking and the disintegration of the Hofstadter butterfly
• Zero modes of the generalized fermion-vortex system in magnetic field
• Non-Abelian Anyon Superconductivity
• Textured Exciton Insulators
• Novel criticality of Dirac fermions from lattice symmetry breaking
• Novel criticality of Dirac fermions in the presence of emergent gauge fields
• Spin-charge Separation in Nodal Antiferromagnetic Insulator
• Superconducting Phases in Lithium Decorated Graphene LiC 6
• To gap or not to gap? Mass distortions and edge modes in graphene armchair nanoribbons
• A Model to Study Finite-Size and Magnetic Effects on the Phase Transition of a Fermion Interacting System
• Topological metals constructed by sliding quantum wire arrays
• Continuous transition between Ising magnetic order and a chiral spin liquid
• Electronic zero modes of vortices in Hall states of gapped graphene
• Magnetic Order-Disorder Transitions on a 1/3 - Depleted Square Lattice
• Self-Organized Bosonic Domain Walls
• Kekulé valence bond order in the honeycomb lattice optical Su-Schrieffer-Heeger Model and its relevance to Graphene
• Non-topological fractional fermion number in the Jackiw-Rossi model
• Trigonal warping, pseudodiffusive transport, and finite-system version of the Lifshitz transition in magnetoconductance of bilayer-graphene Corbino disks
• Equivalence between vortices, twists and chiral gauge fields in Kitaev's honeycomb lattice model
• Noether symmetries and conservation laws of a reduced gauged bilayer graphene model
• Fractionalization in dimerized graphene and graphene bilayer
• Induced fractional valley number in graphene with topological defects
• Color degeneracy of competing orders near topological defects cores in planar quadratic band touching systems
• Logical Majorana zero modes in a nanowire network
• Multipolar spin liquid in an exactly solvable model for $j_{\mathrm{eff}}=\frac{3}{2}$ moments
• Band structure and optical response of Kekulé-modulated $\alpha -{\mathcal{T}}_3$ model
• Non-Abelian vortices in the emergent U(2) gauge theory of the Hubbard model
• Emergent Anti-ferromagnetism in a Y -Shaped Kekulé Graphene
• Topological charge and spin Hall effects due to skyrmions in canted antiferromagnets
• Continued functions and critical exponents: Tools for analytical continuation of divergent expressions in phase transition studies
• Selective branching, quenching, and converting of topological modes
• Optical injection of a spin current into a zigzag nanoribbon of monolayer MoS2 with antiferromagnetic Kekule distortion
• Spin separation and filtering assisted by topological corner states in the Kekulé lattice
• Emergence of Meron Kekulé lattices in twisted Néel antiferromagnets
• Prediction of at topological $p+ip$ excitonic insulator with parity anomaly
• Dynamical properties of quasiparticles in a tunable Kekulé graphene superlattice
• Vortex Solutions and a Novel Role for R-parity in an N=2-Supersymmetric Model for Graphene
• Heavy going
• Disentangling Orbital Magnetic Susceptibility with Wannier Functions
• Critical structure and emergent symmetry of Dirac fermion systems
• Half vortex and fractional electrical charge in two dimensions
• Observation of Embedded Topology in a Trivial Bulk via Projective Crystal Symmetry
• Topological Aspects of Dirac Fermions in a Kagomé Lattice
• Deconfined Fractionally Charged Excitation in Any Dimensions
• Phase transitions on the dark side of the Gross-Neveu model: Spontaneous $\text{O}(4N)$ symmetry breaking at repulsive coupling
• Topological Vortices in Chiral Gauge Theory of Graphene
• Topological quantum control: Edge currents via Floquet depinning of skyrmions in the $\nu =0$ graphene quantum Hall antiferromagnet
• Zero modes and index theorems for non-Hermitian Dirac fermions
• Fractional topological excitations and quantum phase transition in a bilayer 2DEG adjacent to a superconductor film
• Kohn-Luttinger-like mechanism for unconventional charge density waves
• Kekulé order from diffuse nesting near higher-order Van Hove points
• Critical behavior of QED${}_3$--Gross-Neveu-Yukawa Theory in an Arbitrary Gauge
• Physical Properties of the Spin Hamiltonian on Honeycomb Lattice Samples with Kekulé and Vacuum Polarization Corrections
• Charge Fluctuations in Soliton Anti-Soliton Systems Without Conjugation Symmetry
• Periodic Behavior of Topology in Graphene with Nanohole Array
• Interplay of Kekulé distortions and laser fields in graphene
• Single $\pi$-flux hosting topological defect modes in bilayer acoustic metamaterials
• Combined spontaneous symmetry-breaking and symmetry-protected topological order from cluster charge interaction
• Exciton condensation and fractional charge in a bilayer two-dimension electron gas adjacent to a superconductor film
• Wilson loop invariants and bulk-boundary correspondence in higher-order topological insulators with two anticommuting mirror symmetries
• Segregation growth and self-organization of ordered S atomic superlattices confined at interface between graphene and substrates
• Application of Jordan Decomposition to Non-Hermitian Lattice Models with Spectrally-Isolated Lower Dimensional States
• Fermionic criticality with enlarged fluctuations in Dirac semimetals
• Nodal lines in a honeycomb plasmonic crystal with synthetic spin
• Nesting instability of gapless U(1) spin liquids with spinon Fermi pockets in two dimensions