Disorder-Enhanced Dielectric Response of Nanoscale and Mesoscopic Insulators

Enhancement of the dielectric response of insulators by disorder is theoretically proposed, where the quantum interference of electronic waves through the nanoscale or mesoscopic system and its change due to external perturbations control the polarization. In the disordered case with all the states being localized, the resonant tunneling, which is topologically protected, plays a crucial role, and enhances the dielectric response by a factor 30–40 compared with the pure case. The realization of this idea with accessible materials or structures is also discussed.

Figure 1

Ionic dimer system sandwiched by the leads. (a) Transmission and reflection coefficients, $t$ ($t^{\prime }$) and $r$ ($r^{\prime }$) at the left (right) edge of the sample. (b) Ionic level alternation ($Q_1$) and bond dimerization ($Q_2$), and effects of electric field $E$ on the changes $\delta \overrightarrow{Q}$ on $\overrightarrow{Q}$.

Figure 2

Reflectance $R=|r{|}^2$, and the phase $\phi =\arg r$. (a1),(b1): clean bulk system. (a2) (b2): disordered system of finite size $L=401$ with the random potential of the strength $v/t_{\mathrm{n}.\mathrm{n}.}=0.5$. (a3),(b3): disordered system with $L=25$ and a stronger randomness $v/t_{\mathrm{n}.\mathrm{n}.}=2.0$ (see the text). The color code given in (a1),(b1) also applies to (a2,a3), (b2,b3). In the white region in (a1,a2,a3), $R$ is the unity within the accuracy of ${10}^{-4}$. (c1,c2): relative dielectric response in the presence of the disorder compared with the pure case. The disorder strength is $v/t_{\mathrm{n}.\mathrm{n}.}=1.6$ for (c1) and 2.4 for (c2). Averages are taken over ${10}^2$ random disorder configurations. Inside white bands, there occurs a gradual sign change in the dielectric response. (d) Schematic contour mapping of the phase $\phi$ of $r$.