Abstract
An ideal type-III nodal point is generated by crossing a completely flat band and a dispersive band along a certain momentum direction. To date, the type-III nodal points found in two-dimensional (2D) materials have been mostly accidental and random rather than ideal cases, and no one mentions what kind of lattice can produce ideal nodal points. Here, we propose that ideal type-III nodal points can be obtained in a diamond-like lattice. The flat bands in the lattice originate from destructive interference of wavefunctions, and thus are intrinsic and robust. Moreover, the specific lattice can be realized in some 2D carbon networks, such as T-graphene and its derivatives. All the carbon structures possess type-III Dirac points. In two of the structures, consisting of triangular carbon rings, the type-III Dirac points are located just on the Fermi level and the Fermi surface is very clean. Our research not only opens a door to finding the ideal type-III Dirac points, but also provides 2D materials for exploring their physical properties experimentally.
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