Electronic Properties. To probe the

Electronic Properties. To probe the electronic properties of penta-graphene, we calculate its band structure and corresponding total and partial density of states (DOS). As shown in Fig. 4A,penta-graphene is an indirect band-gap semiconductor with a band gap of 3.25 eV [computed using theHeyd–Scuseria–Ernzerhof
(HSE06) functional] (36, 37), because the valance band maximum (VBM) lies on the Γ–X path whereas the conduction band mini-mum is located on the M–Γpath. However, due to the existence of the sub-VBM on the M-Γpath, which is very close to the true VBM in energy, penta-graphene can also be considered as a quasi-direct–
band-gap semiconductor. Analysis of its partial DOS reveals that the electronic states near the Fermi level primarily originate from the sp2 hybridized C2 atoms, which is further confirmed by calculating the band-decomposed charge density distributions,
as shown in Fig. 4B–E. A simplified tight-binding model is used to understand the underlying physics behind the band-gap opening feature in the band structure of penta-graphene (seeSIAppendix,textS3for details). We argue that it is the presence ofthe sp3-hybridized C1 atoms that spatially separates thepz orbitals of sp2 hybridized C2 atoms, hindering full electron delocalization and thus giving rise to a finite band gap. The dispersionless, partially degenerate valance bands lead to a high total DOS near the Fermi level, lending to the possibility that Bardeen–Cooper Schrieffer superconductivity can be achieved in this nanosheet through hole
doping (38)