Dirac cones beyond the honeycomb lattice: A symmetry-based approach

Miert, Guido van; Smith, C. Morais

doi:10.1103/physrevb.93.035401

Cited by 60 publications

(56 citation statements)

References 37 publications

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“…The existence of twelve inequivalent Dirac cones in the low spectrum diagram of a hexagonal lattice can be realized, without resorting to Rashba SOC or twisted bilayer of triangular lattices 17 . Owing to the formation of monolayered ZrB 2 Dirac cones in the lines joining high symmetry points, the cones are not shared with any neighbouring BZ.…”

Section: Discussionmentioning

confidence: 99%

Twelve inequivalent Dirac cones in two-dimensional ZrB2

López-Bezanilla

2018

Phys. Rev. Materials

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Theoretical evidence of the existence of 12 inequivalent Dirac cones at the vicinity of the Fermi energy in monolayered ZrB2 is presented. Two-dimensional ZrB2 is a mechanically stable d-and porbital compound exhibiting a unique electronic structure with two Dirac cones out of high-symmetry points in the irreducible Brillouin zone with a small electron-pocket compensation. First-principles calculations demonstrate that while one of the cones is insensitive to lattice expansion, the second cone vanishes for small perturbation of the vertical Zr position. Internal symmetry breaking with external physical stimuli, along with the relativistic effect of SOC, is able to remove selectively the Dirac cones. A rational explanation in terms of d-and p-orbital mixing is provided to elucidate the origin of the infrequent amount of Dirac cones in a flat structure. The versatility of transition metal d-orbitals combined with the honeycomb lattice provided by the B atoms yields novel features never observed in a two-dimensional material.

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Section: Discussionmentioning

confidence: 99%

Twelve inequivalent Dirac cones in two-dimensional ZrB2

López-Bezanilla

2018

Phys. Rev. Materials

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“…Also, the existence of Dirac fermions in bilayer non-honeycomb crystals using symmetry analysis has been predicted (ref. [18]). …”

Section: Introductionmentioning

confidence: 99%

Fortune teller fermions in two-dimensional materials

2017

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Dirac-like electronic states are the main engines powering the tremendous advances in research of graphene, topological insulators and other materials with these states. Zero effective mass, high carrier mobility and numerous applications are some consequences of linear dispersion that distinguishes Dirac states. Here we report a new class of linear electronic bands in two-dimensional materials with zero effective mass and sharp band edges never seen in solid state matter before, and predict stable materials with such electronic structure utilizing symmetry group analysis and ab initio approach. We make a full classification of completely linear bands in two-dimensional materials and find that only two classes exist: Dirac fermions on one hand and pyramidal-like and cootie catcher-like states on the other hand. The new class supports zero effective mass and hence high carrier mobility similar to that of graphene, anisotropic electronic properties like that of phosphorene, and robustness of states with respect to electronic correlations.

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“…The Dirac cones of 8-Pmmn borophene emerge from this hexagonal lattice which is topologically equivalent to uniaxially strained graphene. If the formation of the Dirac cones along highsymmetry lines in the Brillouin zone is related to the mirror-reflection symmetry of the material [16], it is therefore expected that a distortion of the network from the rectangular to an oblique geometry led likewise to a distortion of the original Dirac cones. Here, we examine the band gap opening obtained upon applying an external shear force to the rectangular cell.…”

Section: Electronic Structurementioning

confidence: 99%