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Note than in literature, different authors frequently use different names referring to this band: interlayer band, free-electron-like band, and even considering it as a trapped first image-potential state of graphene. Upon metal intercalation, its analog is called an intercalant-derived band as well. We agree with Mazin that indeed the definition of the character of such kind of band and corresponding discussion are somewhat philosophical, and just for concreteness in the following will refer to this band as an interlayer band.
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