Electrical permittivity driven metal-insulator transition in heterostructures of nonpolar Mott and band insulators

Metallic interfaces between insulating perovskites are often observed in heterostructures combining polar and nonpolar materials. In these systems, the polar discontinuity across the interface may drive an electronic reconstruction inducing free carriers at the interface. Here, we theoretically show that a metallic interface between a Mott and a band insulator can also form in the absence of a polar discontinuity. The condition for the appearance of such a metallic state is consistent with the classical Mott criterion: the metallic state is stable if the screening length falls below the effective Bohr radius of a particle-hole pair. In this case, the metallic state bears a remarkable similarity to the one found in polar/nonpolar heterostructures. On the other hand, if the screening length approaches the size of the effective Bohr radius, particles and holes are bound to each other resulting in an overall insulating phase. We analyze this metal-insulator transition, which is tunable by the dielectric constant, in the framework of the slave-boson mean-field theory for a lattice model with both on-site and long-range Coulomb interactions. We discuss ground-state properties and transport coefficients, which we derive in the relaxation-time approximation. Interestingly, we find that the metal-insulator transition is accompanied by a strong enhancement of the Seebeck coefficient in the band-insulator region in the vicinity of the interface. The implications of our theoretical findings for various experimental systems such as nonpolar (110) interfaces are also discussed.

Figure 1

Schematic view of the heterostructure studied in this paper. The upper figure is the three-dimensional view of a unit block indicated by the thick lines in the lower. The blue circles represent the electron sites.

Figure 2

The contributions from the MI, the interface (IF), and the BI region to the total conductivity in the large-$U$ limit ($U_{\mathrm{r}}=U-E_{\mathrm{c}}=25t$) as function of the parameter $E_{\mathrm{c}}$ for (a) the polar/nonpolar and (b) the nonpolar/nonpolar heterostructures with $N=10$. The presented IF conductivity is a sum over three (two) layers around the interface for ${\rho }_{\mathrm{c}}=1$ ($\tilde{\rho }=1$), and the MI and BI conductivities are obtained from sums over the remaining inside and outside layers, respectively.

Figure 3

The $U_{\mathrm{r}}-E_{\mathrm{c}}$ phase diagram for the $\tilde{\rho }=1$ nonpolar/nonpolar heterostructure showing the metallic and insulating phases. The solid and dashed lines denote the boundaries between metallic and insulating states for $N=10$ and $N=2$ numbers of MI layers, respectively.

Figure 4

Schematic energy diagram for the insulator with (a) large $U$ and small $E_{\mathrm{c}}$, and (b) large $E_{\mathrm{c}}$ and small $U$.

Figure 5

Distributions of the coherent particle densities $n_{\mathrm{coh}}$. The solid and dashed lines indicate $(U_{\mathrm{r}},E_{\mathrm{c}})=(34.0,1.70)t$ and $(16.2,2.30)t$, respectively.

Figure 6

The distributions of the layer-resolved conductivity ${\sigma }_{\ell }$ and the contribution to the total Seebeck coefficient $S_{\ell }{\sigma }_{\ell }/\sigma$ in the $\tilde{\rho }=1$ nonpolar/nonpolar heterostructure with $U_{\mathrm{r}}=25t$ and $E_{\mathrm{c}}=0.8t,\cdots ,2.0t$. The dashed lines indicate the position of the interfaces, $\ell =-4$ and 5.

Figure 7

(a) The electronic charge distribution $n_{\ell }$ and (b) the effective one-dimensional (1D) electrostatic potential ${\overline{\varphi }}_{\ell }$ for $U_{\mathrm{r}}=25t$ with $E_{\mathrm{c}}=0.8t,\cdots ,2.0t$ around the MI region in the $\tilde{\rho }=1$ structure. The dashed lines indicate the position of the interfaces, $\ell =-4$ and 5.

Figure 8

(a) The amplitude of the double occupancy $d_{\ell }$ and (b) the in-plane-hopping renormalization factor $z_{\ell }^2$ for $U_{\mathrm{r}}=25t$ with $E_{\mathrm{c}}=0.8t,\cdots ,2.0t$ around the MI region in the $\tilde{\rho }=1$ structure. The dashed lines indicate the position of the interfaces, $\ell =-4$ and 5.

Figure 9

The renormalization amplitude of the quasiparticle velocity $Z_{\mathit{k}\nu }$ for $\mathit{k}$ satisfying $E_{\mathit{k}\nu }=\hslash \omega =0$, i.e., $Z_{\nu }^{*}(\omega =0)$, as a function of $E_{\mathrm{c}}$ for $U_{\mathrm{r}}=25t$ in the $\tilde{\rho }=1$ structure.

Figure 10

Square of the wave function at the Fermi energy ${\psi }_{{\mathit{k}}_{\nu }^{*}(\omega =0),\nu }{\left(\ell \right)}^2$ for (a) $E_{\mathrm{c}}=0.80t$ and (b) $E_{\mathrm{c}}=1.90t$, and $U_{\mathrm{r}}=25t$ and $\tilde{\rho }=1$. The dashed lines indicate the position of the interfaces, $\ell =-4$ and 5.

Figure 11

The $\ell =5$ interfacial quantities as a function of $E_{\mathrm{c}}$ for $U_{\mathrm{r}}=25t$ in the $\tilde{\rho }=1$ structure. (a) The electronic charge density $n_{\ell }$, (b) the effective 1D electrostatic potential ${\overline{\varphi }}_{\ell }$, (c) the amplitude of the double occupancy $d_{\ell }$, and (d) the in-plane-hopping renormalization factor $z_{\ell }^2$.

Figure 12

The inverse of the relaxation time at the Fermi energy, ${\tau }_{\nu }^{*}{(\omega =0)}^{-1}$, for $U_{\mathrm{r}}=25t$, $\tilde{\rho }=1$, and ${\gamma }^{\prime }=0$, which means $1/{\tau }_{\nu }^{*}\left(0\right)=2{\gamma }_{\mathit{k}\nu }^{\mathrm{imp}}\left(0\right)/\hslash$ in this figure.

Figure 13

The band-resolved conductivity ${\sigma }_{\nu }$ for $U_{\mathrm{r}}=25t$ and $\tilde{\rho }=1$.

Figure 14

The band-resolved contribution to the total Seebeck coefficient, $S_{\nu }{\sigma }_{\nu }/\sigma$ for $U_{\mathrm{r}}=25t$ and $\tilde{\rho }=1$.