A pseudopotential model for Dirac electrons in graphene with line defects

Эберт, Д.; Zhukovsky, V. Ch.; Stepanov, E. A.

doi:10.1088/0953-8984/26/12/125502

Cited by 12 publications

(16 citation statements)

References 43 publications

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“…The presence of a periodic grain boundary in a graphene flake imposes a discontinuity between the Dirac fermion's spinors on each of the grain boundary's sides. [33][34][35][36] However, grain boundaries that are 3-periodic also connect the two valleys through non-zero intervalley scattering matrix elements. For simplicity, let us consider the case of a zigzag-aligned (i.e.…”

Section: General Properties Of Low-energy Electron Transport Acromentioning

confidence: 99%

“…Similarly, when we set ξ 1 = ξ 2 = ξ and ξ 3 = 0, we recover the case of the zz(558) grain boundary, which owing to its periodicity of 2u 1 also maps the projected Dirac points into distinct values of k x , which ends up blocking intervalley scattering. [31][32][33][34][35][36][37] Moreover, there are a few cases where, despite the 3periodicity of the grain boundary, intervalley scattering is suppressed. In these cases, the microscopic details of the grain boundary, i.e.…”

Section: B the Boundary Condition In The Low-energy Approximationmentioning

confidence: 99%

“…33,34 In alternative, the grain boundary can also be thought of as a finite width strip containing a generalized potential that constrains the dynamics of the massless Dirac fermions. [34][35][36] The specific form of the boundary condition seen by the massless Dirac fermions at the 3-periodic pentagononly grain boundary is determined by the details of its microscopic tight-binding model. In calculating it, we will follow the methodology developed for the cases of the pentagon-only, zz(558) and zz(5757) grain boundaries.…”

Section: Introductionmentioning

confidence: 99%

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Intervalley scattering of graphene massless Dirac fermions at 3-periodic grain boundaries

Rodrigues¹

2016

Phys. Rev. B

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We study how low-energy charge carriers scatter off periodic and linear graphene grain boundaries oriented along the zigzag direction with a periodicity three times greater than that of pristine graphene. These defects map the two Dirac points into the same position, and thus allow for intervalley scattering to occur. Starting from graphene's first-neighbor tight-binding model we show how can we compute the boundary condition seen by graphene's massless Dirac fermions at such grain boundaries. We illustrate this procedure for the 3-periodic pentagon-only grain boundary, and then work out the low-energy electronic scattering off this linear defect. We also compute the effective generalized potential seen by the Dirac fermions at the grain boundary region.

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Section: General Properties Of Low-energy Electron Transport Acromentioning

confidence: 99%

Section: B the Boundary Condition In The Low-energy Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Intervalley scattering of graphene massless Dirac fermions at 3-periodic grain boundaries

Rodrigues¹

2016

Phys. Rev. B

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“…They can be used with different barrier models. 14,[23][24][25] For illustration, we adopt below a model 23 that consists of an effective coupling parameter across the barrier λ and an effective barrier potential parameter ε [cf. Fig.…”

Section: Probing Barrier Transmission In Ballistic Graphenementioning

confidence: 99%

Probing barrier transmission in ballistic graphene

Gunlycke

White

2015

Phys. Rev. B

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We derive the local density of states from itinerant and boundary states around transport barriers and edges in graphene and show that the itinerant states lead to mesoscale undulations that could be used to probe their scattering properties in equilibrium without the need for lateral transport measurements. This finding will facilitate vetting of extended structural defects such as grain boundaries or line defects as transport barriers for switchable graphene resonant tunneling transistors. We also show that barriers could exhibit double minima and that the charge density away from highly reflective barriers and edges scales as $x^{-2}$.Comment: 5 pages and 6 figure

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“…by introducing the phase factor exp(−ie δ i · A) into the hopping term[7]. In a similar way, the scalar potential can be obtained from changing the next-to-nearest hoppings[5,44,43].…”

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confidence: 99%

Phase transitions in hexagonal, graphene-like lattice sheets and nanotubes under the influence of external conditions

et al. 2016

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In this paper we consider a class of (2+1)D schematic models with four-fermion interactions that are effectively used in studying condensed-matter systems with planar crystal structure, and especially graphene. Symmetry breaking in these models occurs due to a possible appearance of condensates. Special attention is paid to the symmetry properties of the appearing condensates in the framework of discrete chiral and C, P and T transformations. Moreover, boundary conditions corresponding to carbon nanotubes are considered and their relations with the effect of an applied external magnetic field are studied. To this end we calculated the effective potential for the nanotube model including effects of finite temperature, density and an external magnetic field. As an illustration we made numerical calculations of the chiral symmetry properties in a simpler Gross-Neveu model with only one condensate taken into account.We also investigated the phase structure of the nanotube model under the influence of the Aharonov-Bohm effect and demonstrated that there is a nontrivial relation between the magnitude of the Aharonov-Bohm phase, compactification of the spatial dimension and thermal restoration of the originally broken chiral symmetry.excitations, closely resembling that of massless relativistic Dirac fermions [5,6]. Combining the two valley degrees of freedom with the two sublattice (pseudospin) degrees of freedom of electrons of carbon atoms, leads in a natural way to a reducible four-component Dirac spinor description in D=(2+1) dimensions. It is just this property which allows for the introduction of a chiral γ 5 -matrix and the use of a chiral (Weyl) representation of Dirac matrices [7].In the continuum limit, the free Dirac Lagrangian of graphene develops an emergent chiral "valley-sublattice" U(2) vs symmetry, which, when considering "multilayer" graphene with N f flavors, is further enlarged to a chiral U(2N f ) symmetry. There arises then the important question, whether the inclusion of fermion interactions can lead to a dynamical breakdown of chiral symmetry with an associated dynamical fermion mass generation and a "semimetalinsulator" phase transition.The phenomenon of a dynamical generation of a fermion mass on the basis of a generic four-fermion interaction is well-known for strong interactions since the time, when Nambu and Jona-Lasinio (NJL) [8] generalized the BCS-Bogoliubov theory [9, 10] of superconductivity to a relativistic model with dynamical breaking of a continuous γ 5 -symmetry. Later on, QCD-motivated NJL-type of models were shown to successfully describe the low-energy meson spectrum of quantum chromodynamics (QCD) [11]. Similar types of four-fermion models with a discrete γ 5 -symmetry have also been considered in lower dimensions D=(1+1) by Gross and Neveu (GN) [12], where the four-fermion theory is renormalizable and asymptotic free, or for D=(2+1) in refs. [13,14]. In the latter case, the model is perturbatively nonrenormalizable but becomes renormalizable in the 1/N f expansion [15].Gener...

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A pseudopotential model for Dirac electrons in graphene with line defects

Cited by 12 publications

References 43 publications

Intervalley scattering of graphene massless Dirac fermions at 3-periodic grain boundaries

Intervalley scattering of graphene massless Dirac fermions at 3-periodic grain boundaries

Probing barrier transmission in ballistic graphene

Phase transitions in hexagonal, graphene-like lattice sheets and nanotubes under the influence of external conditions

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