Generalizing the Fermi velocity of strained graphene from uniform to nonuniform strain

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

doi:10.1016/j.physleta.2015.05.039

Cited by 94 publications

(127 citation statements)

References 57 publications

(98 reference statements)

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“…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 …”

supporting

confidence: 91%

“…In consequence, the effective Dirac Hamiltonian for uniformly strained graphene is of the form

H = ℏ σ \cdot \bar{bold-italicυ} \cdot bold-italicq,

where

true \bar{bold-italicυ}

is the Fermi velocity tensor, q is the momentum measured from the Dirac point and

bold-italicσ = true(τ σ_{x}, σ_{y} true)

is a Pauli matrix vector that acts on the sublattice space, with

τ = \pm

being the valley index. So far the previously reported expressions for

true \overset{bold-italicυ}{true},

as a function on the strain tensor, have been derived without taking into account the effect of the relative displacement vector Δ . However, in order to gain more quantitative knowledge of the strain‐induced effects on graphene, such as optical transmittance modulation, asymmetric Klein tunneling or dynamical gap generation, it is required a precise relationship between strain and the fermion velocity anisotropy.…”

mentioning

confidence: 99%

“…Then, to obtain the effective Dirac Hamiltonian one should expand the tight‐binding Hamiltonian around a Dirac point K D . Thus, an important step within the derivation is the knowledge of the position of K D which is determined by the equation, E ( K D ) = 0, where

E true(bold-italick true) = \pm true| h (bold-italick) true|

is the dispersion relation resulting from Hamiltonian .…”

mentioning

confidence: 99%

See 2 more Smart Citations

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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“…The expression for K D only differs from the derived one in Oliva‐Leyva and Naumis with Δ = 0 in that the vector

A

supporting

confidence: 91%

“…In consequence, the effective Dirac Hamiltonian for uniformly strained graphene is of the form

H = ℏ σ \cdot \bar{bold-italicυ} \cdot bold-italicq,

where

true \bar{bold-italicυ}

is the Fermi velocity tensor, q is the momentum measured from the Dirac point and

bold-italicσ = true(τ σ_{x}, σ_{y} true)

is a Pauli matrix vector that acts on the sublattice space, with

τ = \pm

being the valley index. So far the previously reported expressions for

true \overset{bold-italicυ}{true},

mentioning

confidence: 99%

E true(bold-italick true) = \pm true| h (bold-italick) true|

is the dispersion relation resulting from Hamiltonian .…”

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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show abstract

“…(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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“…23 Several papers have studied transport properties of strained graphene. [24][25][26][27][28][29][30][31][32][33] Optical conductivity, that is, the frequency-dependent conductivity is one of the particular fields which has attracted attention of scientists both experimentally [34][35][36][37] as well as theoretically for further considerations. [38][39][40][41][42][43][44][45] It is necessary to say that important information on the dynamic of carriers (Dirac fermions) in graphene is reported in optical-absorption experiments investigations.…”

Section: Introductionmentioning

confidence: 99%

Strain effects on the optical conductivity of gapped graphene in the presence of Holstein phonons beyond the Dirac cone approximation

Yarmohammadi

2016

AIP Advances

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In this paper we study the optical conductivity and density of states (DOS) of doped gapped graphene beyond the Dirac cone approximation in the presence of electron-phonon (e-ph) interaction under strain, i.e., within the framework of a full π-band Holstein model, by using the Kubo linear response formalism that is established upon the retarded self-energy. A new peak in the optical conductivity for a large enough e-ph interaction strength is found which is associated to transitions between the midgap states and the Van Hove singularities of the main π-band. Optical conductivity decreases with strain and at large strains, the system has a zero optical conductivity at low energies due to optically inter-band excitations through the limit of zero doping. As a result, the Drude weight changes with e-ph interaction, temperature and strain. Consequently, DOS and optical conductivity remains stable with temperature at low e-ph coupling strengths.

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Generalizing the Fermi velocity of strained graphene from uniform to nonuniform strain

Cited by 94 publications

References 57 publications

Theory for Strained Graphene Beyond the Cauchy–Born Rule

Theory for Strained Graphene Beyond the Cauchy–Born Rule

Pseudomagnetic fields and triaxial strain in graphene

Strain effects on the optical conductivity of gapped graphene in the presence of Holstein phonons beyond the Dirac cone approximation

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