Charge inhomogeneities due to smooth ripples in graphene sheets

Juan, Fernando de; Cortijo, Alberto; Vozmediano, María A. H.

doi:10.1103/physrevb.76.165409

Cited by 204 publications

(268 citation statements)

References 33 publications

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“…Equation (5) extends, for a generic static geometry, the Hamiltonian derived in [9,10] for radial and small deformations; see also [11]. Following the notation of [10], the first term in H includes the usual flat Dirac term and the space-dependent Fermi velocity given by the departure from unit of the corresponding "vielben".…”

Section: Dirac Electron In Curved Spacementioning

confidence: 99%

Quantum Field Theory Approach to the Optical Conductivity of Strained and Deformed Graphene

et al. 2015

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The computation of the optical conductivity of strained and deformed graphene is discussed within the framework of quantum field theory in curved spaces. The analytical solutions of the Dirac equation in an arbitrary static background geometry for one dimensional periodic deformations are computed, together with the corresponding Dirac propagator. Analytical expressions are given for the optical conductivity of strained and deformed graphene associated with both intra and interbrand transitions. The special case of small deformations is discussed and the result compared to the prediction of the tight-binding model.

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Section: Dirac Electron In Curved Spacementioning

confidence: 99%

Quantum Field Theory Approach to the Optical Conductivity of Strained and Deformed Graphene

et al. 2015

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“…where g α (ξ 1 , ξ 2 ) is a tangent vector field, δ αβ is the reference (flat) metric andn = g ξ 1 ×g ξ 2 |g ξ 1 ×g ξ 2 | is the local normal [13,23,26,32,33]. However, peculiarities of how graphene ripples [38,39,40,41,42], slides and adheres [39,43] may be beyond first-order continuum elasticity.…”

Section: The Discrete Geometry Of Two-dimensional Materialsmentioning

confidence: 99%

“…The presence of a pseudomagnetic field is observed via broad Landau levels (LLs) in strained graphene nanobubbles on a metal substrate [25]. In addition to the pseudo-magnetic vector potential A s , strain also induces a scalar deformation potential E s [22,26,27] that affects the electron dynamics in non-trivial ways. Part of our motivation was to reconcile the experimental results that can be obtained when the lattice is largely deformed, with a theory that by construction applies to small deformations.…”

Section: A Lattice Gauge Field Theory For Dirac Fermions In Graphenementioning

confidence: 99%

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Discrete differential geometry and the properties of conformal two-dimensional materials

Barraza‐Lopez

2015

Synthetic Metals

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Two-dimensional materials were first isolated no longer than ten years ago, and a comprehensive understanding of their properties under non-planar shapes is still being developed. Strictly speaking, the theoretical study of the properties of graphene and other two-dimensional materials is the most complete for planar structures and for structures with small deformations from planarity. The opposite limit of large deformations is yet to be studied comprehensively but that limit is extremely relevant because it determines material properties near the point of failure. We are exploring uses for discrete differential geometry within the context of graphene and other two-dimensional materials, and these concepts appear promising in linking materials properties to shape regardless of how large a given material deformation is. A brief account of additional contributions arising from our group to two-dimensional materials that include graphene, stanene and phosphorene is provided towards the end of this manuscript.

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“…The deviations of the bulk graphene from a flat surface can also be used to model topological defects [12,13]. In this approach, curvature and torsion are associated with disclinations and dislocations of the medium (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Optical conductivity of curved graphene

Chaves

Frederico

Oliveira

et al. 2014

J. Phys.: Condens. Matter

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Abstract. We compute the optical conductivity for an out-of-plane deformation in graphene using an approach based on solutions of the Dirac equation in curved space. Different examples of periodic deformations along one direction translates into an enhancement of the optical conductivity peaks in the region of the far and mid infrared frequencies for periodicities ∼ 100 nm. The width and position of the peaks can be changed by dialling the parameters of the deformation profiles. The enhancement of the optical conductivity is due to intraband transitions and the translational invariance breaking in the geometrically deformed background. Furthemore, we derive an analytical solution of the Dirac equation in a curved space for a general deformation along one spatial direction. For this class of geometries, it is shown that curvature induces an extra phase in the electron wave function, which can also be explored to produce interference devices of the Aharonov-Bohm type.

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Charge inhomogeneities due to smooth ripples in graphene sheets

Cited by 204 publications

References 33 publications

Quantum Field Theory Approach to the Optical Conductivity of Strained and Deformed Graphene

Quantum Field Theory Approach to the Optical Conductivity of Strained and Deformed Graphene

Discrete differential geometry and the properties of conformal two-dimensional materials

Optical conductivity of curved graphene

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