Extended Data Fig. 6: Modeling layer-inhomogeneous screening in MATNG.
From: Robust superconductivity in magic-angle multilayer graphene family
(a) Schematic of N graphene layers being gated by a top gate (TG) and bottom gate (BG). The electric displacement field between the graphene layers is reduced compared to the field outside the stack due to screening. (b) By assuming a finite density of states \({{{\mathcal{D}}}}\) on each graphene layer, we model the N-layer system as a capacitor network, where \({{{{\rm{c}}}}}_{{{{\rm{q}}}}}={{{{\rm{e}}}}}^{2}{{{\mathcal{D}}}}\) is the quantum capacitance and cg = ε0/d is the geometric capacitance. (c) Calculated electrostatic potential vi on each layer for MATBG, MATTG, MAT4G, MAT5G and MAT6G (N = 2, …, 6), assuming bandwidth W=20 meV, and external displacement field \(\frac{{{{\rm{D}}}}}{{\varepsilon }_{0}}=0.5V/nm\). The twist angle is the same as in Fig. 4, except for 6L which is 1.99°. Here the midplane (the plane of the \(\frac{{{{\rm{N}}}}+1}{2}\)-th layer when N is odd and the midplane between \(\frac{{{{\rm{N}}}}}{2}\)-th layer and (\(\frac{{{{\rm{N}}}}}{2}+1\))-th layer when N is even) is set to be zero both in layer position and in electrostatic potential. For comparison, the electrostatic potential without screening eDdx/ε0 is shown as the dashed line, where \(-\frac{({{{\rm{N}}}}-1)}{2} < {{{\rm{x}}}} < \frac{({{{\rm{N}}}}-1)}{2}\) is the layer position (horizontal axis) and d=0.34 nm is the interlayer distance).
