Hexagonal honeycomb lattice of graphene (a) and its band structure (b). In (b) the equal energy contours are drawn, and the Brillouin zone (BZ) is indicated by dashed lines. The Dirac points K and K′ are marked by arrows, and the reciprocal lattice vectors Ea∗ 1,2 are also drawn. to each cell to construct a Bloch function.
Define lattice. lattice synonyms, lattice pronunciation, lattice translation, English dictionary definition of lattice. n. 1. a. An open framework made of strips of ...
graphene structure: reciprocal lattice reciprocal lattice basis vectors Castro Neto et al., Rev. Mod. Phys 2009 Honeycomb lattice and its corresponding Brillouin zone corners (6) of 1st BZ: K and K' (not equivalent), Dirac points important points for electronic properties (low-energy excitations)
where a= 1.42 ˚A is the physical lattice spacing (lattice constant) of graphene. We ﬁnd ~b 1 ≡ 1 3, 1 √ 3 2π a, (3) ~b 2 ≡ 1 3,− 1 √ 3 2π a. (4) for the reciprocal lattice vectors. The hexagonal lattice can also be described in terms of two triangular lattices (labeled A and B), separated by the vector ~a≡ (~a1 +~a2)/3 as shown in Fig. 1.
2= 2ˇ 3a 1; p 3 (2) We dene the rst Brillouin zone of the reciprocal lattice in the standard way, as bounded 2 by the planes bisecting the vectors to the nearest reciprocal lattice points. This gives a FBZ of the same form as the original hexagons of the honeycomb lattice, but rotated with respect to them by ˇ=2.
In the reciprocal lattice of graphene, there are two types of special points where graphene's valence band and its conduction band crosses with a linear energy-momentum dispersion. Near these points, we need Dirac equation to describe electronic behavior so we call the two types of points as Dirac points.
Graphene 1.9. Reciprocal lattice / Valleys 1.10. Summing up .. Coming up next .. Title: Slide 1 Author: Mindy McCutchan Created Date: 6/3/2015 10:11:05 AM ...
Some 3D Crystal Structures, Reciprocal Lattice, Emergent Dirac Fermion in Graphene . Nearly Free Electron Approximation in Two Dimensions, Twisted Boundary Conditions . de Haas-van Alphen Effect . Bose-Einstein Condensation, Pairing Instability of the Fermi Surface . Berry Phase, Berry Curvature and Chern Number