Curvatronics with bilayer graphene in an effective $4D$ spacetime

Abstract

We show that in AB stacked bilayer graphene low energy excitations around the semimetallic points are described by massless, four dimensional Dirac fermions. There is an effective reconstruction of the 4 dimensional spacetime, including in particular the dimension perpendicular to the sheet, that arises dynamically from the physical graphene sheet and the interactions experienced by the carriers. The effective spacetime is the Eisenhart-Duval lift of the dynamics experienced by Galilei invariant Lévy-Leblond spin $\frac{1}{2}$ particles near the Dirac points. We find that changing the intrinsic curvature of the bilayer sheet induces a change in the energy level of the electronic bands, switching from a conducting regime for negative curvature to an insulating one when curvature is positive. In particular, curving graphene bilayers allows opening or closing the energy gap between conduction and valence bands, a key effect for electronic devices. Thus using curvature as a tunable parameter opens the way for the beginning of curvatronics in bilayer graphene.

8 pages, 3 figures. Revised version with additional material

References in corpus (27)

• The electronic properties of graphene
• The structure of suspended graphene sheets
• A tight-binding approach to uniaxial strain in graphene
• Ab Initio Theory of Gate Induced Gaps in Graphene Bilayers
• Scale-free structural organization of oxygen interstitials in La2CuO4+y
• Holographic duality and the resistivity of strange metals
• Charge inhomogeneities due to smooth ripples in graphene sheets
• Controlling Energy Gap of Bilayer Graphene by Strain
• Electronic properties of curved graphene sheets
• Dirac Equation For Cold Atoms In Artificial Curved Spacetimes
• Ultrafast Dynamics of Massive Dirac Fermions in Bilayer Graphene
• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Revisiting non-relativistic limits
• Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
• Connections and dynamical trajectories in generalised Newton-Cartan gravity I. An intrinsic view
• Thermal mirror buckling in freestanding graphene locally controlled by scanning tunneling microscopy
• Eisenhart lifts and symmetries of time-dependent systems
• Gauge fields in graphene with nonuniform elastic deformations: A quantum field theory approach
• Planar QED at finite temperature and density: Hall conductivity, Berry's phases and minimal conductivity of graphene
• Emergent gravity in the cubic tight-binding model of Weyl semimetal in the presence of elastic deformations
• Tuning Pairing Amplitude and Spin-Triplet Texture by Curving Superconducting Nanostructures
• Perturbation theory of the mass enhancement for a polaron coupled to acoustic phonons
• Hidden symmetries of Eisenhart-Duval lift metrics and the Dirac equation with flux
• Impact of Dresselhaus vs. Rashba spin-orbit coupling on the Holstein polaron
• Conductivity of Dirac fermions with phonon induced topological crossover
• Eisenhart lift for higher derivative systems
• Electron-phonon correlations on spin texture of gapped helical Dirac Fermions

Cited by in corpus (11)

• Embedding Galilean and Carrollian geometries I. Gravitational waves
• Controlling Surface Plasmons Through Covariant Transformation of the Spin-Dependent Geometric Phase Between Curved Metamaterials
• Unruh effect for interacting particles with ultracold atoms
• Different models of gravitating Dirac fermions in optical lattices
• Eisenhart lift for higher derivative systems
• Topological phase-diagram of time-periodically rippled zigzag graphene nanoribbons
• Electronic properties of curved few-layers graphene: a geometrical approach
• Lévy-Leblond fermions on the wormhole
• Lévy-Leblond Equation and Eisenhart-Duval lift in Koopman-von Neumann Mechanics
• Confinement in bilayer graphene via intra- and inter-layer interactions
• The geometry of induced currents in two dimensional media