Figure 1

(Color online) Middle panel: sketch of heterostructure configuration in which narrow-gap insulator (for this paper, a correlated electron compound) is placed between two wide band-gap semiconductors. Left panel: potential drop across heterostructure created by polarization discontinuities at AB and AC interfaces. Right panel: band bending presented as energy $E$ vs momentum $k$ plots at three positions across the heterostructure with chemical potential $\mu$ indicated.Reuse & Permissions

Figure 2

(Color online) Electrostatics of electron-hole liquid formation. Upper panel: $N=3$ layers of polar correlated insulator such as ${\text{LaTiO}}_3$, ${\text{LaVO}}_3$, or ${\text{LaCoO}}_3$ inserted in hypothetical wide band-gap nonpolar insulating host (here ${\text{CaZrO}}_3$) with sheet charge density (in carriers per unit cell) indicated in the ionic picture, along with the induced electric field and the electrostatic potential (in units of the energy $E_c$ defined in the main text. Also shown is the surface dipole required for electrostatic equilibrium, lower panel: $N=3$ layers of a nonpolar correlated insulator such as an infinite-layer cuprate inserted in a polar host with electric field and potential drop indicated. The final surface dipole layer is not shown.Reuse & Permissions

Figure 3

(Color online) Sheet carrier density in units of holes per in-plane unit cell as function of number of Mott insulator layers, computed using parameters appropriate to ${\text{CuO}}_2$ case.Reuse & Permissions

Figure 4

(Color online) Criteria for exciton binding. Left panel: comparison of mean interparticle spacing of electron or hole gas (solid points) computed using bandgap $2\Delta =1.75\text{eV}$ appropriate for high-$T_c$ cuprates. Solid line: interplane distance (assuming interblock spacing is one half of in-lane lattice constant. Right panel: comparison of Drude kinetic energy vs doping (solid points, taken from data summarized in Ref. 35 and Coulomb interaction at scale of interplane spacing $E_{c}a/d_{interplane}$.Reuse & Permissions