Understanding electron behavior in strained graphene as a reciprocal space distortion

Oliva-Leyva, M.; Naumis, Gerardo G.

doi:10.1103/physrevb.88.085430

Cited by 96 publications

(155 citation statements)

References 30 publications

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“…(6) only takes into account the first order corrections in the hopping parameter. Expanding to higher orders in the deformation leads to Fermi surface anisotropy [48,49] and spatially dependent Fermi velocity [50][51][52][53][54][55]. Analogously to a real vector potential, the strain-induced vector potential generates the so-called pseudomagnetic field B s perpendicular to the graphene sheet [2,3].…”

Section: Strain Within Tight-binding Modelsmentioning

confidence: 99%

Pseudomagnetic fields and triaxial strain in graphene

2016

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Pseudomagnetic fields, which can result from nonuniform strain distributions, have received much attention in graphene systems due to the possibility of mimicking real magnetic fields with magnitudes of greater than 100 T. We examine systems with such strains confined to finite regions ("pseudomagnetic dots") and provide a transparent explanation for the characteristic sublattice polarization occurring in the presence of a pseudomagnetic field. In particular, we focus on a triaxial strain leading to a constant field in the central region of the dot. This field causes the formation of pseudo-Landau levels, where the zeroth order level shows significant differences compared to the corresponding level in a real magnetic field. Analytic arguments based on the Dirac model are employed to predict the sublattice and valley dependencies of the density of states in these systems. Numerical tight-binding calculations of single pseudomagnetic dots in extended graphene sheets confirm these predictions, and are also used to study the effect of rotating the strain direction with respect to the underlying graphene lattice, and varying the size of the pseudomagnetic dot.

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Section: Strain Within Tight-binding Modelsmentioning

confidence: 99%

Pseudomagnetic fields and triaxial strain in graphene

2016

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“…Solving

E true({bold-italicK}_{D} true) = 0,

the strain‐induced shift of K D from the corresponding corner K 0 of the first Brillouin zone can be expressed as,

K_{D} = true(true \overset{bold-italicI}{true} - true \overset{bold-italicε}{true} true) \cdot K_{0} + τ bold-italicA,

where

bold-italicA = \frac{β true(1 - κ true)}{2 a} true(ε_{x x} - ε_{y y}, - 2 ε_{x y} true),

and

τ

is the valley index of K 0 . The expression for K D only differs from the derived one in Oliva‐Leyva and Naumis with Δ = 0 in that the vector

A

, an emergent gauge field for nonuniform deformations, is renormalized by a factor (1 − κ ). This result confirms that previously obtained in Midtvedt et al In other words, the position of K D can be obtained by replacing β by β (1 − κ ) in the expression of K D derived without taking into account the effect of the relative displacement vector Δ …”

mentioning

confidence: 86%

Theory for Strained Graphene Beyond the Cauchy–Born Rule

Oliva-Leyva

Wang

2018

Physica Rapid Research Ltrs

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The low‐energy electronic properties of strained graphene are usually obtained by transforming the bond vectors according to the Cauchy–Born rule. In this work, we derive a new effective Dirac Hamiltonian by assuming a more general transformation rule for the bond vectors under uniform strain, which takes into account the strain‐induced relative displacement between the two sublattices of graphene. Our analytical results show that the consideration of such relative displacement yields a qualitatively different Fermi velocity with respect to previous reports. Furthermore, from the derived Hamiltonian, we analyze effects of this relative displacement on the local density of states and the optical conductivity, as well as the implications on the scanning tunneling spectroscopy, including external magnetic field, and optical transmittance experiments of strained graphene.

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“…17 and is used to check the electron behavior. 18 Therefore, the strain-induced lattice distortion and the changed hopping interactions of the two P z orbitals of the neighboring carbon atoms are directly responsible for the electronic structure and transport properties of strained graphene. To make sure that the band gap is opened or not in strained graphene, we plot the band energy structure under different loadings in Fig.…”

Section: Model Of An In-plane Strained Graphenementioning

confidence: 99%

Generalized Hamiltonian for a graphene subjected to arbitrary in-plane strains

Wang

Liu

2015

Funct. Mater. Lett.

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The interplay between the linear elastic deformation up to 20% and the unique electronic properties of graphene nanostructures offers an attractive prospect to manipulate their properties by strain. Here we review the recent progress on the electronic response of graphene to the in-plane strains, including the strain-modulated electronic structure and the strain-modulated spin, valley and superconducting transports. A generalized Hamiltonian for a graphene was constructed subjected to arbitrary in-plane strains. The Hamiltonian is helpful to design and optimize the graphene-based nano-electromechanical systems (NEMS).

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Understanding electron behavior in strained graphene as a reciprocal space distortion

Cited by 96 publications

References 30 publications

Pseudomagnetic fields and triaxial strain in graphene

Pseudomagnetic fields and triaxial strain in graphene

Theory for Strained Graphene Beyond the Cauchy–Born Rule

Generalized Hamiltonian for a graphene subjected to arbitrary in-plane strains

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