Merging of Dirac points in a two-dimensional crystal
By G. Montambaux, F. Piéchon, J. Fuchs, M. Goerbig. 2009
233 citations recorded by the source corpus.
We study under which general conditions a pair of Dirac points in the electronic spectrum of a twodimensional crystal may merge into a single one. The merging signals a topological transition between a semimetallic phase and a band insulator. We derive a universal Hamiltonian that describes the physical properties of the transition, which is controlled by a single parameter, and analyze the Landau-level spectrum in its
Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/da97dccc531b5f0bc9808dd6d5e95e893293e45c
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In Atomic and Molecular Physics, and Optics
In Materials Chemistry
Citations in the corpus
- Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene (2018, background): “This case is a topological Lifshitz transition in which two Dirac cones with opposite topological charge merge and annihilate, as predicted for standard s band graphene [4,45] and reported in photonic [7,8] and atomic [5,6] honeycomb lattices and in black phosphorus [9].”
- Electronic properties of graphene in a strong magnetic field (2010, background): “…the vicinity of the transition, one may expand the Hamiltonian (59) around the merging point M ′′ (Montambaux et al., 2009a,b), and one finds6 HMq = ( 0 ∆ + ~ 2q2x 2m∗ − i~cqy ∆+ ~ 2q2x 2m∗ + i~cqy 0 ) , (64) in terms of the mass m∗ = 2~2/3ta2 and the velocity c = 3ta/~ (Montambaux et al., 2009b).”
- Gauge fields for ultracold atoms in optical superlattices (2009, background): “However, their topological robustness [54] might be affected by small deviations from α = 1/2 that break the two-site periodicity.”
- Exciton-polaritons in lattices: A non-linear photonic simulator (2016, background): “Merging of the Dirac cones [18,107,108], artificial gauge fields [29,109] and the appearance of novel edge states [28] can now be studied in a platform with unprecedented nonlinearities.”
- Novel effects of strains in graphene and other two dimensional materials (2015, background): “It also arises when applying uniaxial strain in the zigzag direction, a situation that has been discussed at length in the literature [58, 106, 244, 363].”
- Topological photonics (2018, background): “The first case was theoretically studied by Montambaux et al. (2009).”
- Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice (2011, background): “The relative strength of the tunnel couplings between the different sites of the lattice fixes the position of the Dirac points inside the Brillouin zone, as well as the slope of the associated linear dispersion relation [5–9].”