Symmetry-induced band-gap opening in graphene superlattices

Martinazzo, Rocco; Casolo, Simone; Tantardini, Gian Franco

doi:10.1103/physrevb.81.245420

Cited by 100 publications

(96 citation statements)

References 49 publications

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“…The different behavior of these two classes (multiples of 3 or not of the primitive cell of the pristine system) of graphene superlattices is now wellunderstood in terms of the energy band-folding model. [55][56][57] Indeed, even in pure graphene, when p is a multiple of 3, the two Dirac points K and K ′ in the primitive cell are folded to the Γ point of the hexagonal first-Brillouin zone (BZ) of the superlattice, giving rise to a fourfold degeneracy that can be broken, opening a band gap, by a periodic arrangement of defects. In the other case, the twofold degenerate Dirac points do not fold into Γ and a band gap opening can be induced by breaking the inversion symmetry.…”

Section: Resultsmentioning

confidence: 99%

Inducing a Finite In-Plane Piezoelectricity in Graphene with Low Concentration of Inversion Symmetry-Breaking Defects

et al. 2015

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We show that a finite in-plane piezoelectricity can be induced in graphene by breaking its inversion center with any in-plane defect, in the limit of vanishing defect concentration. We first consider different patterns of BN-doped graphene sheets of D 3h symmetry, whose electronic and piezoelectric (dominated by the electronic rather than nuclear term) properties are characterized at the ab initio level of theory. We then consider other in-plane defects, such as holes of D 3h or C 2v point-symmetry, and confirm that a common limit value (for low defect concentration) of the piezoelectric response of graphene is obtained regardless of the particular chemical or physical nature of the defects (e 11 ≈ 4.5 × 10 −10 C/m and d 11 ≈ 1.5 pm/V for direct and * To whom correspondence should be addressed † Equipe de Chimie Physique, IPREM UMR5254, Université de Pau et des Pays de l'Adour, 64000 Pau, France ‡ Chemistry Department, Faculty of Science, Minia University, Minia 61519, Egypt ¶ Dipartimento di Chimica and Centre of Excellence NIS (Nanostructured Interfaces and Surfaces), Università di Torino, via Giuria 5, IT-10125 Torino (Italy) 1 converse piezoelectricity, respectively). This in-plane piezoelectric response of graphene is one-order of magnitude larger than the out-of-plane previously investigated one.

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Section: Resultsmentioning

confidence: 99%

Inducing a Finite In-Plane Piezoelectricity in Graphene with Low Concentration of Inversion Symmetry-Breaking Defects

et al. 2015

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“…This case demonstrates the crucial role played by the intrinsic symmetry of the pattern in determining the electronic structure. [11][12][13] Let us now take a closer look at the triangular patterns of adatom groups that have hexagonal symmetry. In Fig.…”

Section: Adatom Patterned Graphene Nanomeshesmentioning

confidence: 99%

“…9,10 Using symmetry arguments and tight binding calculations, it was shown that the periodic structure of defects (such as B and N impurities) on graphene can exhibit semimetallic and semiconductor behavior. 11 Moreover, a weak perturbation potential forming a large hexagonal lattice in a two-dimensional (2D) electron gas was shown to lead to a massless Dirac fermion Hamiltonian with linearly crossing bands at Dirac points. [12][13][14] The majority of the current studies on graphene is devoted to its chemical modification to create derivatives with different structures and properties.…”

Section: Introductionmentioning

confidence: 99%

Structural, mechanical, and electronic properties of defect-patterned graphene nanomeshes from first principles

Şahin

Çiraci

2011

Phys. Rev. B

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Motivated by the state of the art method for fabricating high-density periodic nanoscale defects in graphene, the structural, mechanical, and electronic properties of defect-patterned graphene nanomeshes including diverse morphologies of adatoms and holes are investigated by means of first-principles calculations within density functional theory. It is found that various patterns of adatom groups yield metallic or semimetallic, even semiconducting, behavior and specific patterns can be in a magnetic state. Even though the patterns of single adatoms dramatically alter the electronic structure of graphene, adatom groups of specific symmetry can maintain the Dirac fermion behavior. Nanoholes forming nanomesh are also investigated. Depending on the interplay between the repeat periodicity and the geometry of the hole, the nanomesh can be in different states ranging from metallic to semiconducting including semimetallic states with the bands crossing linearly at the Fermi level. We showed that forming periodically repeating superstructures in a graphene matrix can develop a promising technique for engineering nanomaterials with desired electronic and magnetic properties.

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“…By looking at the total values of the direct piezoelectric constant, it is seen that for small dopant concentrations the common asymptotic value of approximately 5×10 −10 C/m is reached for all systems, 21 Let us just briefly recall that this is due to the fact that the band gap of the system varies with defect concentration according to two distinct behaviors depending on whether the considered superlattice is or not a multiple of 3 of the primitive cell of pristine graphene, as predicted by the energy band-folding model. [52][53][54] As a further consideration, we might notice that the vibrational contribution is always smaller in absolute value than the electronic one, which is found to dominate the in-plane piezoelectric response of functionalized graphene.…”

Section: In-plane Piezoelectricitymentioning

confidence: 99%

Piezoelectricity of Functionalized Graphene: A Quantum-Mechanical Rationalization

et al. 2016

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A large out-of-plane piezoelectricity can be induced in graphene by carbon substitution. Several simple substitutions are considered where C atoms are replaced by heavier group-IV elements (Si, Ge and Sn). A more complex functionalization (namely, pyrrolic N-doped graphene)is also investigated where different functional groups, such as F, Cl, H 3 C and H 2 N, are studied. Piezoelectric and elastic response properties of all systems are determined quantummechanically at the ab initio level of theory. A rationalization of the physical and chemical parameters which most affect the out-of-plane piezoelectricity of functionalized graphene is reported, which reveals the dominant character of the nuclear over electronic contribution. The combination of an out-of-plane symmetry-breaking defect and a soft infrared-active phonon mode, with a large cell-deformation coupling, is shown to constitute the necessary prerequisite to induce a large out-of-plane piezoelectric response into functionalized graphene.

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Symmetry-induced band-gap opening in graphene superlattices

Cited by 100 publications

References 49 publications

Inducing a Finite In-Plane Piezoelectricity in Graphene with Low Concentration of Inversion Symmetry-Breaking Defects

Inducing a Finite In-Plane Piezoelectricity in Graphene with Low Concentration of Inversion Symmetry-Breaking Defects

Structural, mechanical, and electronic properties of defect-patterned graphene nanomeshes from first principles

Piezoelectricity of Functionalized Graphene: A Quantum-Mechanical Rationalization

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