Low-energy theory for strained graphene: an approach up to second-order in the strain tensor

Oliva-Leyva, M.; Wang, Chumín

doi:10.1088/1361-648x/aa62c9

Cited by 26 publications

(35 citation statements)

References 59 publications

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“…where ν is the Poisson ratio. [4,10] Therefore, v ? slightly increases with the increasing of ϵ: However, from the more general expression (9), it follows that…”

Section: Effective Dirac Hamiltonianmentioning

confidence: 98%

“…For example, to reveal the trigonal anisotropy due to the underlying honeycomb lattice is needed a study up to second order in the strain tensor. [10] On the other hand, note that making κ ¼ 0 reduces equation (9)…”

Section: Effective Dirac Hamiltonianmentioning

confidence: 99%

“…www.advancedsciencenews.com www.pss-rapid.com A simple exploration shows that equation (15) reproduces, for κ ¼ 0, the previous results obtained within the approximation Δ ¼ 0. [8,10] Moreover, such as occur for the position of the Dirac points, the more general conductivity tensor (15) can be obtained from the expression for the optical conductivity derived in Oliva-Leyva and Naumis [8] by means of the simple replacement β ! β (1 À κ).…”

Section: Effective Dirac Hamiltonianmentioning

confidence: 99%

“…In particular, it is worth mentioning that the principal axes of

true \bar{bold-italicυ}

are collinear with the ones of the strain tensor

true \overset{bold-italicε}{true},

because the electronic anisotropy is only caused by the deformation. For example, to reveal the trigonal anisotropy due to the underlying honeycomb lattice is needed a study up to second order in the strain tensor . On the other hand, note that making

κ = 0

reduces equation to

\bar{υ} = v_{0} true[true \overset{bold-italicI}{true} + true \overset{bold-italicε}{true} - β true \overset{bold-italicε}{true} true],

which is the Fermi velocity tensor derived without considering Δ .…”

mentioning

confidence: 99%

“…To illustrate this issue, let us to consider graphene subjected a uniaxial strain of stretching magnitude

ε

along an arbitrary direction. According to the approximation

\bar{υ} = v_{0} true[true \overset{bold-italicI}{true} + true \overset{bold-italicε}{true} - β true \overset{bold-italicε}{true} true],

the Fermi velocity perpendicular to the stretching direction is given by

ν_{⊥} = ν_{0} true[1 + (β - 1) normalν bold-italicε true],

where

normalν

is the Poisson ratio . Therefore,

v_{⊥}

slightly increases with the increasing of

ε .

However, from the more general expression , it follows that

v_{⊥} = v_{0} true[1 + (β - 1) normalν ε - β κ (1 + ν) ε /2 true] .

But if

true(β - 1 true) ν < β κ true(1 + normalν true) / 2

as occurred for graphene, then

v_{⊥}

slightly decreases with the increasing of the stretching magnitude

…”

mentioning

confidence: 99%

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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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“…where ν is the Poisson ratio. [4,10] Therefore, v ? slightly increases with the increasing of ϵ: However, from the more general expression (9), it follows that…”

Section: Effective Dirac Hamiltonianmentioning

confidence: 98%

Section: Effective Dirac Hamiltonianmentioning

confidence: 99%

Section: Effective Dirac Hamiltonianmentioning

confidence: 99%

“…In particular, it is worth mentioning that the principal axes of

true \bar{bold-italicυ}

are collinear with the ones of the strain tensor

true \overset{bold-italicε}{true},

κ = 0

reduces equation to

\bar{υ} = v_{0} true[true \overset{bold-italicI}{true} + true \overset{bold-italicε}{true} - β true \overset{bold-italicε}{true} true],

which is the Fermi velocity tensor derived without considering Δ .…”

mentioning

confidence: 99%

“…To illustrate this issue, let us to consider graphene subjected a uniaxial strain of stretching magnitude

ε

along an arbitrary direction. According to the approximation

\bar{υ} = v_{0} true[true \overset{bold-italicI}{true} + true \overset{bold-italicε}{true} - β true \overset{bold-italicε}{true} true],

the Fermi velocity perpendicular to the stretching direction is given by

ν_{⊥} = ν_{0} true[1 + (β - 1) normalν bold-italicε true],

where

normalν

is the Poisson ratio . Therefore,

v_{⊥}

slightly increases with the increasing of

ε .

However, from the more general expression , it follows that

v_{⊥} = v_{0} true[1 + (β - 1) normalν ε - β κ (1 + ν) ε /2 true] .

But if

true(β - 1 true) ν < β κ true(1 + normalν true) / 2

as occurred for graphene, then

v_{⊥}

slightly decreases with the increasing of the stretching magnitude

…”

mentioning

confidence: 99%

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Theory for Strained Graphene Beyond the Cauchy–Born Rule

Oliva-Leyva

Wang

2018

Physica Rapid Research Ltrs

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Magneto-optical conductivity of anisotropic two-dimensional Dirac–Weyl materials

Oliva-Leyva

Wang

2017

Annals of Physics

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In the presence of an external magnetic field, the optical response of two-dimensional materials, whose charge carriers behave as massless Dirac fermions with arbitrary anisotropic Fermi velocity, is investigated. Using Kubo formalism, we obtain the magneto-optical conductivity tensor for these materials, which allows to address the magneto-optical response of anisotropic Dirac fermions from the well known magneto-optical conductivity of isotropic Dirac fermions. As an application, we analyse the combined effects of strain-induced anisotropy and magnetic field on the transmittance, as well as on the Faraday rotation, of linearly polarized light after passing strained graphene. The reported analytical expressions can be a useful tool to predict the absorption and the Faraday angle of strained graphene under magnetic field. Finally, our study is extended to anisotropic two-dimensional materials with Dirac fermions of arbitrary pseudospin.

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Landauer-Büttiker conductivity for spatially-dependent uniaxial strained armchair-terminated graphene nanoribbons

Espinosa-Champo

Roman‐Taboada

Naumis

2018

Physica E: Low-dimensional Systems and Nanostructures

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The Landauer-Büttiker conductivity of arbitrary uniaxial spatially dependent strain in an armchair graphene nanoribbon is studied. Due to the uniaxial character of the strain, the corresponding transfer matrix can be reduced to a product of 2 × 2 matrices. Then the conductivity and the Fano factor can be calculated from this product. As an example of the technique, sinusoidal space dependent strain fields are studied using two different strain wavelengths. For the bigger wavelength the conductivity is reduced when compared with the unstrained case, although both conductivities are almost the same in shape. Whereas, for the smaller wavelength case, the conductivity is strongly modified. In spite of this, for energies close to the Dirac point energy, the conductivity and the Fano factor are quite similar to their unstrained counterpart for the two strain wavelengths here studied.

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Low-energy theory for strained graphene: an approach up to second-order in the strain tensor

Cited by 26 publications

References 59 publications

Theory for Strained Graphene Beyond the Cauchy–Born Rule

Theory for Strained Graphene Beyond the Cauchy–Born Rule

Magneto-optical conductivity of anisotropic two-dimensional Dirac–Weyl materials

Landauer-Büttiker conductivity for spatially-dependent uniaxial strained armchair-terminated graphene nanoribbons

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