Generalized Dirac structure beyond the linear regime in graphene

Iorio, Alfredo; Pais, P.; Elmashad, I. A.; Ali, Ahmed Farag; Faizal, Mir; Abou-Salem, L. I.

doi:10.1142/s0218271818500803

Cited by 57 publications

(76 citation statements)

References 35 publications

(72 reference statements)

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“…where we used in the second line the property [C, AB] = {C, A}B − A{C, B} for A, B, C arbitrary matrices, and also the Clifford algebra (13) in the third line.…”

Section: Appendix C: Generators J Abmentioning

confidence: 99%

“…We have learned, first theoretically [1][2][3] and then experimentally [4,5] that graphene, and other materials [6][7][8], realize "spinors quasi-particles", i.e., particles whose Dirac or Weyl properties emerge due to the structure of the space (lattice) with which the electrons interact. We have also learned how the emergence of intrinsic as well as extrinsic curvature in graphene can be used to probe the fundamental physics of the quantum Dirac field theory in the presence of a variety of curved, but torsion-free, spacetimes [9][10][11] (see also the review [12]) and even to probe certain quantum gravity scenarios [13], (see also [14,15]).…”

Section: Introductionmentioning

confidence: 99%

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(Anti-)de Sitter, Poincaré, Super symmetries, and the two Dirac points of graphene

Iorio

Pais

2018

Annals of Physics

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We propose two different high-energy-theory correspondences with graphene (and related materials) scenarios, associated to grain boundaries, that are topological defects for which both Dirac points are necessary. The first correspondence points to a (3 + 1)-dimensional theory, with nonzero torsion, with spatiotemporal gauge group SO(3, 1), locally isomorphic to the Lorentz group in (3 + 1) dimensions, or to the de Sitter group in (2 + 1) dimensions. The other correspondence treats the two Dirac fields as an internal symmetry doublet, and it is linked here with unconventional supersymmetry with SU (2) internal symmetry. Our results are suggestive, rather than conclusive, and pave the way to the inclusion of grain boundaries in the emergent field theory picture associated with these materials, whereas disclinations and dislocations have been already well explored.

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“…where we used in the second line the property [C, AB] = {C, A}B − A{C, B} for A, B, C arbitrary matrices, and also the Clifford algebra (13) in the third line.…”

Section: Appendix C: Generators J Abmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

(Anti-)de Sitter, Poincaré, Super symmetries, and the two Dirac points of graphene

Iorio

Pais

2018

Annals of Physics

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“…We rewrite the overall interaction as a sum of interactions between subsequent orders of neighbors, and go up to the m th -near neighbors. It can be shown [5] that the field Hamiltonian (1) becomes…”

Section: Dirac Structure Beyond the Linear Regimementioning

confidence: 99%

“…In [5] the result up to order O( 2 ) is given. This is a rich algebraic structure, worth investigating, especially in relation to the possibility for noncommutativity.…”

Section: Dirac Structure Beyond the Linear Regimementioning

confidence: 99%

Generalized uncertainty principle in graphene

Iorio

Pais

2019

J. Phys.: Conf. Ser.

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We show that, by going beyond the low-energy approximation for which the dispersion relations of graphene are linear, the corresponding emergent field theory is a specific generalization a Dirac field theory. The generalized Dirac Hamiltonians one obtains are those compatible with specific generalizations of the uncertainty principle. We also briefly comment on the compatibility of the latter with noncommuting positions, [x i , x j ] = 0, and on their possible physical realization.

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“…In the last years, due to their low energy spectrum structure, Dirac materials [9] have emerged as experimental playgrounds where both kinds of arenas, the fundamental research and the condensed matter one, met. In particular, the role of disclinations is under intense investigation to realize graphene analogs of Dirac quantum fields in curved spacetimes, see, e.g., [10][11][12][13][14][15][16] and recently the role of yet another kind of defects (grain boundaries) was also explored [17]. Investigations on how, in this context, dislocations could be used to construct an analog Dirac field theory coupled with torsion, rather than curvature, were of course carried on, see, e.g., [18].…”

Section: Introductionmentioning

confidence: 99%

Torsion in quantum field theory through time-loops on Dirac materials

et al. 2020

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Assuming dislocations could be meaningfully described by torsion, we propose here a scenario based on the role of time in the low-energy regime of two-dimensional Dirac materials, for which coupling of the fully antisymmetric component of the torsion with the emergent spinor is not necessarily zero. Appropriate inclusion of time is our proposal to overcome well-known geometrical obstructions to such a program, that stopped further research of this kind. In particular, our approach is based on the realization of an exotic time-loop, that could be seen as oscillating particle-hole pairs. Although this is a theoretical paper, we moved the first steps toward testing the realization of these scenarios, by envisaging Gedankenexperiments on the interplay between an external electromagnetic field (to excite the pair particle-hole and realize the time-loops), and a suitable distribution of dislocations described as torsion (responsible for the measurable holonomy in the time-loop, hence a current). Our general analysis here establishes that we need to move to a nonlinear response regime. We then conclude by pointing to recent results from the interaction lasergraphene that could be used to look for manifestations of the torsion-induced holonomy of the time-loop, e.g., as specific patterns of suppression/generation of higher harmonics. 1 In the following we refer to two dimensional Dirac materials, with hexagonal lattice. Examples are graphene, germanene, silicene [9]. 2 We use Latin indices a; b; … for tangent/flat space and Greek indices μ; ν; … for base curved manifold. We choose the signature η ab ¼ diagðþ; −; −Þ. The Vielbeins are denoted by e a μ and their inverse by E μ a .3 This is due to the reducible, rather than irreducible, representation of the Lorentz group we use. CIAPPINA, IORIO, PAIS, and ZAMPELI PHYS. REV. D 101, 036021 (2020) 036021-2 FIG. 2. Idealized time-loop. At t ¼ 0, the hole (yellow) and the particle (black) start their journey from y ¼ 0, in opposite directions. Evolving forward in time, at t ¼ t Ã > 0, the hole reaches −y Ã , while the particle reaches þy Ã , (blue portion of the circuit). Then they come back to the original position, y ¼ 0, at t ¼ 2t Ã (red portion of the circuit). This can be repeated indefinitely. On the far right, the equivalent time-loop, where the hole moving forward in time is replaced by a particle moving backward in time.

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Generalized Dirac structure beyond the linear regime in graphene

Cited by 57 publications

References 35 publications

(Anti-)de Sitter, Poincaré, Super symmetries, and the two Dirac points of graphene

(Anti-)de Sitter, Poincaré, Super symmetries, and the two Dirac points of graphene

Generalized uncertainty principle in graphene

Torsion in quantum field theory through time-loops on Dirac materials

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