Emergent Horava gravity in graphene

Volovik, G. E.; Zubkov, M. A.

doi:10.1016/j.aop.2013.11.003

Cited by 58 publications

(86 citation statements)

References 49 publications

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“…Then, to obtain the effective Dirac Hamiltonian one should expand the tight-binding Hamiltonian (4) around a Dirac point K D . [21,22] Thus, an important step within the derivation is the knowledge of the position of K D which is determined by the equation,…”

Section: Effective Dirac Hamiltonianmentioning

confidence: 99%

“…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%

“…So far the previously reported expressions for υ; as a function on the strain tensor, have been derived without taking into account the effect of the relative displacement vector Δ. [19][20][21][22] However, in order to gain more quantitative knowledge of the strain-induced effects on graphene, such as optical transmittance modulation, [23] asymmetric Klein tunneling [24] or dynamical gap generation, [25,26] it is required a precise relationship between strain and the fermion velocity anisotropy.…”

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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Section: Effective Dirac Hamiltonianmentioning

confidence: 99%

“…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%

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 calculations envisage the influence of g and α on the coefficients. Namely, the magnetic field dependence on resistivity ρ xx and ρ xy depicts that the bigger values of α one takes the smaller resistivity we achieve.In general one expects the presence of additional gauge fields in graphene due to geometric and other reasons [32,33]. The use of gauge/gravity duality allows for the exact solution of the strongly coupled field theoretical models.…”

mentioning

confidence: 99%

Conductivity bound of the strongly interacting and disordered graphene from gauge/gravity duality

Rogatko

Wysokiński

2020

Phys. Rev. D

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The carriers in graphene tuned close to the Dirac point envisage signatures of the strongly interacting fluid and are subject to hydrodynamic description. The important question is whether strong disorder induces the metal -insulator transition in this two-dimensional material. The bound on the conductivity tensor found earlier within the single current description, implies that the system does not feature metal -insulator transition. The linear spectrum of the graphene imposes the phase -space constraints and calls for the two -current description of interacting electron and hole liquids. Based on the gauge/gravity correspondence, using the linear response of the black brane with broken translation symmetry in Einstein-Maxwell gravity with the auxiliary U (1)-gauge field, responsible for the second current, we have calculated the lower bound of the DC-conductivity in holographic model of graphene. The calculations show that the bound on the conductivity depends on the coupling between both U (1) fields and for a physically justified range of parameters it departs only weakly from the value found for a model with the single U (1) field. * Electronic address: marek.rogatko@poczta.umcs.lublin.pl, rogat@kft.umcs.lublin.pl † Electronic address: karol.wysokinski@poczta.umcs.pl 2 shown to facilitate high mobility transport at temperatures below 150K. The recent theoretical and experimental studies of hydrodynamic effect in graphene have been reviewed in [21,22].Even though the hydrodynamic flow is expected to be observed in a very clean system, the disorder seems to be an important factor which sometimes even facilitates the hydrodynamic behavior [23]. The signatures of the Stokes non-linear flow with the low Reynolds number [24] have been detected in graphene [25], as the appearance of vortices leading to the negative resistance of the material.At the Fermi level graphene exhibits a massless relativistic spectrum with Dirac cone. As was mentioned above, close to the charge neutrality point, it sustains a strongly interacting material, ideal system for studies by means of gauge/gravity duality methods. In this system, the thermoelectric transport coefficients have been found using the hydrodynamic approach [26][27][28], with a fairly good agreement with the experimental data.Recently, this attitude has been generalized to the model with two distinct U (1)-gauge currents, which is solved by the AdS/CFT analogy [29]. The model in question allowed the successful quantitative comparison between theory and experimental data. The paper [29] gives a number of arguments behind the introduction of two gauge fields and associated currents. One reason for the appearance of two currents in graphene is the charge imbalance between electrons and holes in the system with linear spectrum. It has been found that the two current model allows for a quantitatively correct description of the thermal conductance of graphene. The paper [30] presented the further generalization, taking into account the possible coupling between both currents....

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Effects of a Uniform Magnetic Field on Twisted Graphene Nanoribbons

et al. 2023

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In the present work, the relativistic quantum motion of massless fermions in a helicoidal graphene nanoribbon under the influence of a uniform magnetic field is investigated. Considering a uniform magnetic field (B) aligned along the axis of helicoid, this problem is explored in the context of Dirac equation in a curved space-time. As this system does not support exact solutions due to considered background, the bound-state solutions and local density of states (LDOS) are obtained numerically by means of the Numerov method. The combined effects of width of the nanoribbon (D), length of ribbon (L), twist parameter (𝝎), and B on the equations of motion and LDOS are analyzed and discussed. It is verified that the presence of B produces a constant minimum value of local density of state on the axis of helicoid, which is possible only for values large enough of 𝝎, in contrast to the case for B = 0 already studied in the literature.

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Emergent Horava gravity in graphene

Cited by 58 publications

References 49 publications

Theory for Strained Graphene Beyond the Cauchy–Born Rule

Theory for Strained Graphene Beyond the Cauchy–Born Rule

Conductivity bound of the strongly interacting and disordered graphene from gauge/gravity duality

Effects of a Uniform Magnetic Field on Twisted Graphene Nanoribbons

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