Figure 1

The charge transfer $\Delta n_{\alpha =1}=n_{\alpha =1}-n$ between the surface layer ($\alpha =1$) and the bulk as a function of the filling $n$ for uniform $t$.Reuse & Permissions

Figure 2

(left) Occupation $n$ vs $(\mu -U/2)/W$ for two different values of interaction strength $U/W$. The data shown are for the bulk system and the surface layer with uniform $t$. The plateau in the occupation at $n=1$ signals the onset of the incompressible Mott state. (right) Surface-layer quasiparticle weight $z_1$ for uniform $t$ and the bulk quasiparticle weight as a function of occupation. The solid line shows $z$ for the bulk calculation.Reuse & Permissions

Figure 3

Plot of the quasiparticle weight $z$ vs electron density $n$ near half-filling for (top) $U/W=1.5$ and (bottom) $U/W=2.0$. The bulk result is given by the solid black curve. The corresponding result for the surface layer is given by the red dashed curve with open squares; the value of $z$ at the surface is significantly reduced from that in the bulk. Since the coordination number is lower on the surface, then the surface electrons effectively experience a large Coulomb repulsion. If this is the primary reason for the reduced value of $z$, then a bulk calculation with a larger value of $U$ should mimic the original result at the surface. This is clearly not the case, even when we double the value of $U$. In the bottom panel we instead lower the value of $U_1$ (on the surface) in an attempt to restore a value of $z$ equal to that in the bulk; this is also unsuccessful, indicating that charge transfer effects are an important ingredient for the reduced quasiparticle weight on the surface.Reuse & Permissions

Figure 4

The charge transfer $\Delta n_{\alpha =1}=n_{\alpha =1}-n$ between the surface layer ($\alpha =1$) and the bulk as a function of the filling $n$ for $t_{12}/t=0.5$ and $t_{11}/t=0.5$ at $T=0.0$.Reuse & Permissions

Figure 5

(left) Occupation $n$ vs $(\mu -U/2)/W$ for two different values of interaction strength $U/W$. The data shown are for the bulk system and the surface layer with $t_{12}/t=0.5$ and $t_{11}/t=0.5$. The plateau in the occupation at $n=1$ signals the onset of the incompressible Mott state. (right) Surface layer quasiparticle weight $z_1$ for nonuniform $t$ and the bulk quasiparticle weight as a function of occupation. The solid line shows $z$ for the bulk calculation.Reuse & Permissions

Figure 6

The quasiparticle weight plotted vs electron density. The open squares joined by the solid black line denote the bulk weight as a function of the bulk electron density; this shows a characteristic decrease from $n\approx 0$ to half-filling, where an insulating state is present. The surface quasiparticle weight $z_1$ (filled red squares joined by dashed red line) is shown vs the same bulk electron density and shows considerable variation from the bulk. The same quantity, but plotted vs the surface electron density, is shown by open circles joined by the green short-dashed line. This result is in qualitative agreement with the bulk result. An improvement is achieved by accounting for the effective higher Coulomb repulsion, as described in the text; this is shown with open triangles joined by the pink dot-dashed line; this result is in excellent quantitative agreement with the renormalized surface quasiparticle weights. We have used $t_{11}/t=0.5$ for the calculations shown in this plot.Reuse & Permissions