Field-induced metal-insulator transition and switching phenomenon in correlated insulators

We study the nonequilibrium switching phenomenon associated with the metal-insulator transition under electric field $E$ in correlated insulators by a gauge-covariant Keldysh formalism. Due to the feedback effect of the resistive current $I$, this occurs as a first-order transition with a hysteresis of $I\text{−}V$ characteristics having a lower threshold electric field $\left(\sim {10}^4\text{V}{\text{cm}}^{-1}\right)$ much weaker than that for the Zener breakdown. It is also found that the localized midgap states introduced by impurities and defects act as hot spots across which the resonant tunneling occurs selectively, which leads to the conductive filamentary paths and reduces the energy cost of the switching function.

Figure 1

(Color online) The tilted band structure under an external electric field $E$. At each spatial position $R$, the momentum $p$ is defined as shown in the orthogonal direction. The conduction-band bottom and the valence-band top cross the energy $\omega =0$ at $R_2$ and $R_1$, respectively. The localized impurity state represented by the peak at $R=R_{\text{imp}}$ gives rise to the resonant tunneling.

Figure 2

(Color online) (a) The right-hand side of gap equation (4), $\overline{⟨c_{p,R}^{†}{c}_{p,L}⟩}/2$, in unit of $\Gamma /10\hslash v$ as a function of the gap $\Delta$ for $\zeta /\xi =eE\hslash v/4{\Delta }_0^2=0.0,0.8,1.2$, with $\Gamma$ being the energy cutoff, i.e., the half bandwidth of the equilibrium states. Here, ${\Delta }_0$ is the gap in the equilibrium for $g=5\hslash v$. The solid straight line represents $\Delta /g$ in the same unit and the crossing of these two gives the solution(s) to mean-field equation (4). (b) The obtained current $I$ as a function of the electric field $E$. The dashed line is a guide for the eyes. The $I\text{−}E$ characteristics clearly show the hysteresis and switching behavior of the current. The red dotted curve represents the current obtained for the fixed gap ${\Delta }_0$.

Figure 3

(Color online) The $\text{Im}\left({\widehat{G}}^A{\Delta }_0\right)$ as a function of the normalized energy $\omega /{\Delta }_0$ (${\Delta }_0$: the energy gap in the equilibrium) for $\zeta /\xi =6.4$ (dotted line), 3.2 (solid line), and 0.4 (dashed line) ($\zeta =\hslash v/2{\Delta }_0$: correlation length, $\xi =2{\Delta }_0/eE$).