Tunable Type-I and Type-II Dirac Fermions in Graphene with Nitrogen Line Defects

Abstract

Recently, type-II Dirac fermions characterized by strongly titled Dirac cones have been proposed. The new fermions exhibit unique physical properties different from the type-I Dirac fermions in graphene, and thus attract tremendous attentions. Up to date, all type-II fermions are only found in the heavy compounds with strong spin obit coupling. Here, we propose that both type-I and type-II Dirac fermions can exist in the graphene embedding nitrogen line defects. While the types of Dirac fermions are determined by the size W of graphene nanoribbons between the line defects. By comparing the two types of Dirac fermions, their different physical properties and originations are revealed directly. Remarkably, the type-I Dirac points induce one Fermi arc corresponding to edge states along the armchair direction, while the type-II Dirac points induce two Fermi arcs corresponding to two sets of edge states along the zigzag direction. These results not only expand our views on the Dirac fermions in two-dimensional structures, but also extend their applications in electronics.

Cp-Graphyne: A Low-Energy Graphyne Polymorph with Double Distorted Dirac Points

“…The heteroatomic networks (janugraphene and chlorographene) 11 coupled with the rectangular lattices and nonequivalent bonds also possess Dirac points. Graphene with nitrogen line defects, 46 Ni 2 C 18 H 12 , and Co 2 C 18 H 12 47 are some of the 2D materials with linear band dispersion relation in their electronic band structures. This indicates that there is an immense interest in exploring novel materials with Dirac points.…”

Theoretical prediction of low-energy Stone-Wales graphene with an intrinsic type-III Dirac cone

“…Recently, Dirac-cones with highly anisotropic property have attracted tremendous attentions as the great importance for the direction-dependent optical and electronic properties. It is reported that the anisotropic band dispersions can be induced in graphene through external Periodic Potentials 42,43 or elemental doping 45 . In fact, intrinsic anisotropic Dirac-cones can be realized through graphene allotropes 23,32,33 and graphyne allotropes 31,41,46,47 , such as OPG-Z 33 , phagraphene 32 and SW-graphene 23 .…”

Novel 2D PC5 with a Dirac Cone and Edge‐Size Dependence

“…There are other similar rules found when carbon atoms are assembled into hexagonal lattices. [ 68–72 ] . For instance, after the dopant atoms N, B, S, Al, Si, and P are periodically doped in graphenes, there is a zero gap or a neglectable gap at the Dirac point when its primitive cell is ( N is an integer).…”

“…For instance, after the dopant atoms N, B, S, Al, Si, and P are periodically doped in graphenes, there is a zero gap or a neglectable gap at the Dirac point when its primitive cell is ( N is an integer). [ 68 ] Doping along the linear direction in graphenes has been studied in previous works; [ 69,73,74 ] there is a rule found in the nitrogen‐molecule‐doped graphene system. [ 69 ] When and ( N is an integer), the structures have type‐I Dirac cones around the Fermi level, while they have type‐II Dirac cones when .…”

“…[ 68 ] Doping along the linear direction in graphenes has been studied in previous works; [ 69,73,74 ] there is a rule found in the nitrogen‐molecule‐doped graphene system. [ 69 ] When and ( N is an integer), the structures have type‐I Dirac cones around the Fermi level, while they have type‐II Dirac cones when . The structures in these linear doping systems contain pentagonal, hexagonal, and octagonal rings, whereas the structure in our work only has hexagonal rings.…”