Geometrical and topological aspects of graphene and related materials

Abstract

Graphene, a two-dimensional crystal made of carbon atoms, provides a new and unexpected bridge between low and high-energy physics. The field has evolved very fast and very good reviews are already available in the literature. Graphene constitutes a condensed matter realization of lower dimensional quantum field theory models that were proposed to confront important -- still unresolved -- puzzles of the area: Chiral symmetry breaking and quark confinement. The new materials named topological insulators, closely related to graphene, are physical realizations of topological field theory. This article reviews some of these topics with the aim of bridging the gap and making these condensed matter issues accessible to high energy readers. The electronic interactions in the monolayer are analyzed with special emphasis on the recent experimental confirmation of some theoretical predictions. The issue of spontaneous chiral symmetry breaking in the model materials is also reviewed. Finally we give an extensive description of some recent topological aspects of graphene that allow to understand the main aspects of topological insulators.

Review to appear in J. Phys. A

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• Control of graphene's properties by reversible hydrogenation
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• Topological Field Theory of Time-Reversal Invariant Insulators
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• Biased bilayer graphene: semiconductor with a gap tunable by electric field effect
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• Infrared spectroscopy of Landau levels in graphene
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• Scanning Tunneling Spectroscopy of Graphene on Graphite
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• Electron fractionalization in two-dimensional graphenelike structures
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• Is graphene in vacuum an insulator?
• Cyclotron Resonance study of the electron and hole velocity in graphene monolayers
• Interaction-Driven Spectrum Reconstruction in Bilayer Graphene
• The Coulomb impurity problem in graphene
• On the $Z_2$ classification of Quantum Spin Hall Models
• Vacuum Polarization and Screening of Supercritical Impurities in Graphene
• Pseudospin Magnetism in Graphene
• Effects of topological defects and local curvature on the electronic properties of planar graphene
• Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
• Many-body interactions in quasi-freestanding graphene
• Charge inhomogeneities due to smooth ripples in graphene sheets
• Lattice field theory simulations of graphene
• Chiral Gauge Theory for Graphene
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• The Schwinger mechanism and graphene
• Localized states at zigzag edges of bilayer graphene
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• Graphene via large N I: Renormalization
• Electronic properties of curved graphene sheets
• Interacting fermions on the honeycomb bilayer: from weak to strong coupling
• Minimal conductivity in graphene: interaction corrections and ultraviolet anomaly
• Spin-orbit coupling in a graphene bilayer and in graphite
• UV fixed-point structure of the three-dimensional Thirring model
• Conductivity of interacting massless Dirac particles in graphene: Collisionless regime
• Chiral Symmetry Breaking in Graphene
• Oscillatory multiband dynamics of free particles: The ubiquity of zitterbewegung effects
• Manifestations of topological effects in graphene
• Electron Interactions in Bilayer Graphene: Marginal Fermi Liquid Behaviour and Zero Bias Anomaly
• Variational approach to the excitonic phase transition in graphene
• Non-Fermi Liquid behavior in Neutral Bilayer Graphene
• Topological aspects of graphene: Dirac fermions and the bulk-edge correspondence in magnetic fields
• Renormalization group aspects of graphene
• Finite volume effects and dynamical chiral symmetry breaking in QED3

Cited by in corpus (42)

• On the Phase Structure of Many-Flavor QED${}_3$
• Charge instabilities and topological phases in the extended Hubbard model on the honeycomb lattice with enlarged unit cell
• Critical behavior of the (2+1)-dimensional Thirring model
• Ising and Gross-Neveu model in next-to-leading order
• Topologically non-trivial valley states in bilayer graphene quantum point contacts
• Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry
• Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
• Chiral anomaly in Dirac semimetals due to dislocations
• Emergent gravity in the cubic tight-binding model of Weyl semimetal in the presence of elastic deformations
• Random gauge field effects on the conductivity of graphene sheets with disordered ripples
• Landau-Khalatnikov-Fradkin transformations in Reduced Quantum Electrodynamics
• Comments on the Chern-Simons photon term in the QED description of graphene
• Symmetry Breaking and Lattice Kirigami
• Influence of interactions on the anomalous quantum Hall effect
• Momentum dependence of quantum critical Dirac systems
• Unconventional Supersymmetry at the Boundary of AdS_4 Supergravity
• Fermionic vacuum currents in topologically nontrivial braneworlds: Two-brane geometry
• Symmetry breaking and lattice kirigami: finite temperature effects
• The Casimir effect for fermionic currents in conical rings with applications to graphene ribbons
• Superconducting phase transitions induced by chemical potential in (2+1)-dimensional four-fermion quantum field theory
• A Note on Bloch theorem
• Charge density and conductivity of disordered Berry-Mondragon graphene nanoribbons
• Topological order and Berry connection for the Maxwell Vacuum on a four-torus
• Excitonic Instabilities and Insulating States in Bilayer Graphene
• Wightman function and the Casimir effect for a Robin sphere in a constant curvature space
• Effect of topological defects and Coulomb charge on the low energy quantum dynamics of gapped graphene
• Aspects of the pseudo Chiral Magnetic Effect in 2D Weyl-Dirac Matter
• Floquet analysis of pulsed Dirac systems: A way to simulate rippled graphene
• Dynamical Casimir Effect in a small compact manifold for the Maxwell vacuum
• The type II Weyl semimetals at low temperatures: chiral anomaly, elastic deformations, zero sound
• Classical and quantum dynamics of a kicked relativistic particle in a box
• Aharonov-Bohm phases in a quantum LC circuit
• Topological Casimir effect in a quantum LC circuit: real-time dynamics
• Zeroes of combinations of Bessel functions and mean charge of graphene nanodots
• Effects of a uniform magnetic field on twisted graphene nanoribbons
• The Casimir effect for nonlinear sigma models and the Mermin-Wagner-Hohenberg-Coleman theorem
• Pauli-Term-Induced Fixed Points in $d$-dimensional QED
• Chiral magnetic effect at finite temperature in a field-theoretic approach
• Topological and superconducting properties of two-dimensional C6-2x(BN)x biphenylene network: a first-principles investigation
• Analytic solution for Gauged Dirac-Weyl equation in $(2+1)$-dimensions
• Gauge fields induced by curved spacetime
• Domain wall interactions due to vacuum Dirac field fluctuations in 2+1 dimensions