Figure 1

Electron density $n(x)$ (upper panel) and potential $V(x)$ (lower panel) in a metal-SCES interface with (a) $V_{\infty }=-2.25$, (b) $V_{\infty }=-1$, and (c) $V_{\infty }=-0.5$ ($U/t=4$, $n_{+}=0.7$, $\alpha =0.043$, and $L=100$). In each panel, a description of each region is given in the top where dark (white) regions are insulator (metal), e.g., band insulator (BI), metal (M), and Mott insulator (MI). The schematic picture in the left-lower space describes the bending of the upper (lower) Hubbard band UH (LH) near the interface. $E_{\mathrm{F}}$ is the Fermi energy.Reuse & Permissions

Figure 2

(a) Universal density-potential relation of the 1D interface Mott transition. Electron density $n(x)$, $51\le x\le 90$ is plotted against $-[V(x)-V_{\infty }]$. $V_{\infty }$ is varied from $V_{\infty }=-3.00$ to $V_{\infty }=0$ with an interval of 0.25. $W(U)$ is the bandwidth and $\Delta (U)$ the width of the $n=1$ plateau. Inset: The $U$ dependence of $\Delta (U)$. This is determined from data with density $n\in [0.96,1.04]$ (open circle) and $n\in [0.98,1.02]$ (open boxes). The solid line is the Mott gap from Lieb-Wu’s solution [13]. (b) The width of the Mott insulating ($d_{\mathrm{MI}}$, $n\in [0.85,1.04]$; blue), metallic ($d_{\mathrm{M}}$, $n\in [1.04,1.96]$; red) and band insulating ($d_{\mathrm{BI}}$, $n\in [1.96,2.0]$; green) layers plotted against $V_{\mathrm{D}}$. The symbols are DMRG results while the solid lines are the solutions of Poisson’s equation [Eqs. (4, 5, 6)].Reuse & Permissions

Figure 3

(a) Density-potential relation near Mott’s transition in dimensions higher than one (schematic). A region ($V_1<V<V_2$) exists where metallic and insulating phases coexist. (b) $I\mathrm{\text{−}}V$ characteristics of the metal-SCES interface when $V_1<V_{\mathrm{D}}+V_{\infty }<V_2$ is satisfied. Pictures of the off state (c) and on state (d).Reuse & Permissions