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Volumn 77, Issue 19, 2008, Pages

Characterization of graphene through anisotropy of constant-energy maps in angle-resolved photoemission

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EID: 43049106087     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.77.195403     Document Type: Article
Times cited : (171)

References (51)
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    • The tight-binding parameters are defined as γ0 =- ΦA1 | H | ΦB1 =- ΦA2 | H | ΦB2 , where ΦA1 is an atomic orbital located on A1 site, γ1 =+ ΦA2 | H | ΦB1 , γ3 =+ ΦA1 | H | ΦB2 , and γ4 =+ ΦA1 | H | ΦA2 =+ ΦB1 | H | ΦB2 . These definitions agree with those of the Slonczewski-Weiss-McClure model of graphite (Refs.). Note that the parameters describing interlayer hopping (γ1, γ3, and γ4) enter the Hamiltonian of the Slonczewski-Weiss-McClure model with an additional factor of 2 that takes into account the greater number of neighboring graphene planes in bulk graphite as compared to bilayer graphene.
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    • For emission from the conduction band at very low energy (top left side of Fig. 5), the interference pattern has two peaks [roughly similar to cos2 (φ)], but one of the peaks has about three times stronger maximum intensity than the others. The reason is that corrections due to the presence of dimer orbitals are small (in parameter q /vq) but finite (this band has α=+1). Their influence may be estimated by considering the function g (φ) =1+cos (2φ) +4 (q /vq) cos (φ) +2 (q /vq) 2 [Eq. 10]. Comparing the maxima of the two peaks, at angles φ=0 and φ=π, gives g (0) /g (π) = [(1+ q /vq) / (1- q /vq)] 2. For the energy considered on the top left side of Fig. 5, where q ≈ 2 v2 q2 / γ1, then q /vq≈ (q / γ1) 1/2 ≈0.29. Thus, although this is "small," it yields g (0) /g (π) ≈3.34.
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    • ARPES spectra as described in Secs. 3 3 corresponding to photons with low energies, such that pz d 1 (d is the interlayer spacing), are the same for both twin crystals. To apply the results of Sec. 3 to the B2-A1 twin, one would have to invert the signs of Δ and U. For higher photon energies, such that β= pz d is finite, the anisotropy maps in Fig. 9 of Sec. 3 should be reflected with respect to the horizontal axis.
    • ARPES spectra as described in Secs. 3 3 corresponding to photons with low energies, such that pz d 1 (d is the interlayer spacing), are the same for both twin crystals. To apply the results of Sec. 3 to the B2-A1 twin, one would have to invert the signs of Δ and U. For higher photon energies, such that β= pz d is finite, the anisotropy maps in Fig. 9 of Sec. 3 should be reflected with respect to the horizontal axis.


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