Thus, the hopping term from site 2 to 1 is

, from site 3

Thus, the hopping term from site 2 to 1 is

, from site 3 to 4 is , from site 4 to 3 is , and from site 5 to 6 is . With the above four hopping terms, we thus have (3) which means that the effective direct hopping parameter between sites 1 and 6 is (4) The obtained effective hopping parameter has the same sign as t 1, which means that pseudospin in α-graphdiyne has the same direction as in graphene. Thus, many perspectives P505-15 cell line of graphene can be transferred to α-graphdiyne directly. The magnitude of depends on the hopping parameter t 2. Remarkably, it equals t 1/t 2 times the effective hopping parameter in α-graphyne. Thus, the effective hopping parameter should be smaller in α-graphdiyne than in α-graphyne as t 1/t 2 < 1. Once we obtain the effective hopping parameter , the standard energy-momentum relation can be obtained directly as [1] (5) where a is the lattice constant. By fitting the occupied and unoccupied bands in the vicinity of the K point from the first-principles Quisinostat mw calculations, as illustrated in Figure 2a, the renormalized hopping parameter has a value of 0.45 eV. It is much smaller than the value of approximately 3 eV in graphene, which originates from the larger lattice constant in α-graphdiyne. Figure 2c shows the high-symmetry learn more points in the first Brillouin zone. It explicitly

shows that the energy bands are degenerate to zero at both K and K ′ points. In Figure 2d, a 2D plot of the Dirac cone of α-graphdiyne is displayed. Due to the same hexagonal lattice as graphene and α-graphyne, the

2D Dirac cone of α-graphdiyne exhibits a similar appearance. It is known that the Fermi velocity plays a vital role in the photoelectric field and crucially Megestrol Acetate dominates the transport properties. Here, we will focus attention on the study of Fermi velocity of α-graphdiyne. The dispersion close to the K and K ′ points can be expanded as (6) where q is the momentum measured relative to the Dirac points, ‘ ±’ the upper and lower Dirac cones, and v F the Fermi velocity, given by . With the lattice constant a = 11.42 Å and the effective hopping parameter = 0.45 eV, the slope of the Dirac cone in α-graphdiyne equals ±4.5 eVÅ compared with ±28 eVÅ in α-graphyne and ±34 eVÅ in graphene [4]. The corresponding Fermi velocity is about 0.11 ×106 m/s, which is much lower than the value in α-graphyne. From this perspective, α-graphdiyne, which has a lower Fermi velocity than other known carbon allotropes, will lead to possible applications in quantum electrodynamics, for example, to observe the anomalous integer quantum Hall effect at room temperature [13]. More information including the helical texture of Dirac cone and Berry’s phase are indeed associated with the detailed wave functions. In this work, we instead calculate the two orbitals at the Dirac point as shown in Figure 3.

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