Tight-binding theory of spin-orbit coupling in graphynes

Miert, Guido van; Juričić, Vladimir; Smith, C. Morais

doi:10.1103/physrevb.90.195414

Cited by 38 publications

(28 citation statements)

References 36 publications

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“…In α-GDY, we also observed the appearance of both occupied and empty flat bands, another typical topology-dependent feature found for 2D COFs. 23 − 26 …”

Section: Resultsmentioning

confidence: 99%

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Designing All Graphdiyne Materials as Graphene Derivatives: Topologically Driven Modulation of Electronic Properties

et al. 2021

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Designing new 2D systems with tunable properties is an important subject for science and technology. Starting from graphene, we developed an algorithm to systematically generate 2D carbon crystals belonging to the family of graphdiynes (GDYs) and having different structures and sp/sp 2 carbon ratios. We analyze how structural and topological effects can tune the relative stability and the electronic behavior, to propose a rationale for the development of new systems with tailored properties. A total of 26 structures have been generated, including the already known polymorphs such as α-, β-, and γ-GDY. Periodic density functional theory calculations have been employed to optimize the 2D crystal structures and to compute the total energy, the band structure, and the density of states. Relative energies with respect to graphene have been found to increase when the values of the carbon sp/sp 2 ratio increase, following however different trends based on the peculiar topologies present in the crystals. These topologies also influence the band structure, giving rise to semiconductors with a finite band gap, zero-gap semiconductors displaying Dirac cones, or metallic systems. The different trends allow identifying some topological effects as possible guidelines in the design of new 2D carbon materials beyond graphene.

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“…In α-GDY, we also observed the appearance of both occupied and empty flat bands, another typical topology-dependent feature found for 2D COFs. 23 − 26 …”

Section: Resultsmentioning

confidence: 99%

“…Such phenomena observed in the electronic structure of COFs have been explained based on peculiar topological effects also in connection to their influence on the charge transport behavior. 23 − 26 …”

Section: Introductionmentioning

confidence: 99%

Designing All Graphdiyne Materials as Graphene Derivatives: Topologically Driven Modulation of Electronic Properties

et al. 2021

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“…Here we do not find any stable fixed point, leading us to the prediction that a triple point appears with first-order transitions only. While in our description the number of fermion flavors has been introduced merely as a theoretical control parameter, a similar deformation of the honeycomb lattice system should be relevant for the novel systems with a large number of Dirac cones [70].…”

Section: Discussionmentioning

confidence: 99%

Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization

et al. 2016

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We study the competition of spin-and charge-density waves and their quantum multicritical behavior for the semimetal-insulator transitions of low-dimensional Dirac fermions. Employing the effective Gross-Neveu-Yukawa theory with two order parameters as a model for graphene and a growing number of other two-dimensional Dirac materials allows us to describe the physics near the multicritical point at which the semimetallic and the spin-and charge-density-wave phases meet. With the help of a functional renormalization group approach, we are able to reveal a complex structure of fixed points, the stability properties of which decisively depend on the number of Dirac fermions N f . We give estimates for the critical exponents and observe crucial quantitative corrections as compared to the previous first-order expansion. For small N f , the universal behavior near the multicritical point is determined by the chiral Heisenberg universality class supplemented by a decoupled, purely bosonic, Ising sector. At large N f , a novel fixed point with nontrivial couplings between all sectors becomes stable. At intermediate N f , including the graphene case (N f = 2) no stable and physically admissible fixed point exists. Graphene's phase diagram in the vicinity of the intersection between the semimetal, antiferromagnetic and staggered density phases should consequently be governed by a triple point exhibiting first-order transitions.

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“…More importantly, -graphyne becomes a topological insulator under SOC with an induced gap of 0.59 meV and a Z 2 topological invariant of 1 v  [103]. A TB approach to investigate SOC effect in more graphynes has been developed, and rich phase transitions were predicted [104][105]. Besides designing new graphynes, another way to construct Dirac systems is tuning the structure of known graphynes.…”

Section: Graphynesmentioning

confidence: 99%

The rare two-dimensional materials with Dirac cones

Wang

Deng

Liu

2015

National Science Review

386

229

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Note: This manuscript has been published as Natl. Sci. Rev. 2 (1), 22-39 (2015), refer to: http://nsr.oxfordjournals.org/content/2/1/22.full ABSTRACT Inspired by the great development of graphene, more and more works have been conducted to seek new two-dimensional (2D) materials with Dirac cones. Although 2D Dirac materials possess many novel properties and physics, they are rare compared with the numerous 2D materials. To provide explanation for the rarity of 2D Dirac materials as well as clues in searching for new Dirac systems, here we review the recent theoretical aspects of various 2D Dirac materials, including graphene, silicene, germanene, graphynes, several boron and carbon sheets, transition metal oxides (VO 2 ) n /(TiO 2 ) m and (CrO 2 ) n /(TiO 2 ) m , organic and organometallic crystals, so-MoS 2 , and artificial lattices (electron gases and ultracold atoms). Their structural and electronic properties are summarized. We also investigate how Dirac points emerge, move, and merge in these systems. The von Neumann-Wigner theorem is used to explain the scarcity of Dirac cones in 2D systems, which leads to rigorous requirements on the symmetry, parameters, Fermi level, and band overlap of materials to achieve Dirac cones. Connections between existence of Dirac cones and the structural features are also discussed.

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Tight-binding theory of spin-orbit coupling in graphynes

Cited by 38 publications

References 36 publications

Designing All Graphdiyne Materials as Graphene Derivatives: Topologically Driven Modulation of Electronic Properties

Designing All Graphdiyne Materials as Graphene Derivatives: Topologically Driven Modulation of Electronic Properties

Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization

The rare two-dimensional materials with Dirac cones

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