(Anti-)de Sitter, Poincaré, Super symmetries, and the two Dirac points of graphene

Abstract

We propose two different high-energy-theory correspondences with graphene (and related materials) scenarios, associated to grain boundaries, that are topological defects for which both Dirac points are necessary. The first correspondence points to a $(3+1)$-dimensional theory, with nonzero torsion, with spatiotemporal gauge group $SO(3,1)$, locally isomorphic to the Lorentz group in $(3+1)$ dimensions, or to the de Sitter group in $(2+1)$ dimensions. The other correspondence treats the two Dirac fields as an internal symmetry doublet, and it is linked here with unconventional supersymmetry with $SU(2)$ internal symmetry. Our results are suggestive, rather than conclusive, and pave the way to the inclusion of grain boundaries in the emergent field theory picture associated with these materials, whereas disclinations and dislocations have been already well explored.

arXiv comment37 pages, 10 figures, relevant references included, typos corrected

References in corpus (32)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Weyl and Dirac Semimetals in Three Dimensional Solids
• The Black Hole in Three Dimensional Space Time
• Topological Materials: Weyl Semimetals
• Gauge fields in graphene
• Electronic Properties of Graphene in a Strong Magnetic Field
• Topological Defects in Graphene: Dislocations and Grain Boundaries
• Physical Aspects of the Space-Time Torsion
• Observation of quantum Hawking radiation and its entanglement in an analogue black hole
• Polycrystalline graphene and other two-dimensional materials
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Novel effects of strains in graphene and other two dimensional materials
• Experimental signatures of the mixed axial-gravitational anomaly in the Weyl semimetal NbP
• The Electronic Spectrum of Fullerenes from the Dirac Equation
• Effects of topological defects and local curvature on the electronic properties of planar graphene
• Thermal Hadronization and Hawking-Unruh Radiation in QCD
• Dimensionally Reduced Gravitational Chern-Simons Term and its Kink
• The Hawking-Unruh phenomenon on graphene
• Dislocations and torsion in graphene and related systems
• Curved Spacetimes and Curved Graphene: a status report of the Weyl-symmetry approach
• Supersymmetry of a different kind
• Parallel Transport of Electrons in Graphene Parallels Gravity
• Revisiting the gauge fields of strained graphene
• Generalized Dirac structure beyond the linear regime in graphene
• Quantum gravity with torsion and non-metricity
• Comments on the Chern-Simons photon term in the QED description of graphene
• Supersymmetric 3D model for gravity with $SU(2)$ gauge symmetry, mass generation and effective cosmological constant
• Dynamical Contents of Unconventional Supersymmetry
• Unconventional Supersymmetry at the Boundary of AdS_4 Supergravity
• On the implications of the Bekenstein bound for black hole evaporation
• Dispersionless wave packets in Dirac materials

Cited by in corpus (19)

• Generalized Uncertainty Principle in three-dimensional gravity and the BTZ black hole
• $\mathcal{N}$-Extended $D=4$ Supergravity, Unconventional SUSY and Graphene
• Torsion in quantum field theory through time-loops on Dirac materials
• Hunting Quantum Gravity with Analogs: the case of graphene
• Generalized uncertainty principle in graphene
• Torsion at different scales: from materials to the Universe
• The three "layers" of graphene monolayer and their analog generalized uncertainty principles
• Curvature-induced pseudogauge fields from time-dependent geometries in graphene
• Turning graphene into a lab for noncommutativity
• Reduced quantum electrodynamics in curved space
• Two arguments for more fundamental building blocks
• Massless Rarita-Schwinger equations: Half and three halves spin solution
• Relational Supersymmetry via the Dressing Field Method and Matter-Interaction Supergeometric Framework
• Unconventional Supersymmetry via the Dressing Field Method
• Quantum black holes as classical space factories
• Quantum Charged Spinning Massless Particles in 2+1 dimensions
• Fractional vorticity, Bogomol'nyi-Prasad-Sommerfield systems and complex structures for the (generalized) spinor Gross-Pitaevskii equations
• Time-loops to spot torsion on bidimensional Dirac materials with dislocations
• Micropolar continua as projective space of Skyrmions