Figure 4

Potential profiles depending on dopant arrangement. (a) The red line indicates the spatial variation of the potential energy ψ(x) in BLG on NH₂-SAMs. NH₂ ⁺- and NH₂-AS are distinguished by ⊕ and ○. ψ(x) shows the minimum on NH₂ ⁺-AS and changes spatially in accord with the characteristic screening length l _SC,//. The blue curves show the band structure E(k) modified by ψ(x). The horizontal plane indicates the Fermi energy E _F at the charge neutrality point around V _bg ~ −65 V. At a position far from NH₂ ⁺-AS, i.e., the position corresponding to the middle energy diagram, ψ(x) is mainly affected by V _bg ~ −65 V. The negative V _bg produces a downward electric field to open the band gap. Nonetheless, E _F is located at the valence band, producing a hole puddle. However, at a position just above NH₂ ⁺-AS, i.e., the position corresponding to the left or right energy diagram, the effect of NH₂ ⁺-AS is larger than that of V _bg, producing an upward electric field. In this case, E _F is located in the conduction band, producing an electron puddle. In this way, both hole and electron puddles contribute to carrier transport at the charge neutrality point. (b) NH₂ ⁺-AS and F₄TCNQ⁻ molecules, denoted by ⊕ and \(\ominus \), are aligned in the normal direction. The horizontal plane indicates E _F at the charge neutrality point around V _bg ~ 0 V. Two red dashed curves show the potential energy produced by each molecule, which mutually cancel. In this case, the perpendicular electric field produces the band gap, which directly affects the transport property at the charge neutrality point. (c) NH₂ ⁺-AS and F₄TCNQ⁻ molecules are not aligned. The horizontal plane indicates E _F at the charge neutrality point around V _bg ~ 0 V. When the lateral spacing of two dopants is larger than l _SC,//, the potential energy produced by each molecule is not cancelled but varies with location. In this case, the transport property is determined by electron and hole puddles as in (a). The different arrangement in (b and c) originates in the magnitude of potential variation and the screening length l _SC,//.