Metallization of Nanofilms in Strong Adiabatic Electric Fields

We introduce an effect of metallization of dielectric nanofilms by strong, adiabatically varying electric fields. The metallization causes optical properties of a dielectric film to become similar to those of a plasmonic metal (strong absorption and negative permittivity at low optical frequencies). This is a quantum effect, which is exponentially size-dependent, occurring at fields on the order of $0.1\mathrm{V}/\AA$ and pulse durations ranging from $\sim 1\mathrm{fs}$ to $\sim 10\mathrm{ns}$ for a film thickness of 3–10 nm.

Figure 1

Field effect on electron states: spectrum, localization, transmission, and mixing. The data are for an $N=30$ (9 nm) nanofilm thickness. (a) Energy bands of infinite crystal (lines) and nanofilm (dots) in zero electric field. Bands are color-coded by green (localized band), red (valence band), and blue (conduction band). (b) Energy bands of nanofilm as a function of the applied electric field (color-coded as above). (c) Valence band levels in electric field $\mathcal{E}=0.06\mathrm{V}/\AA$. The black lines and state notations are discussed in the text. (d) The same as in (c) but for $\mathcal{E}=0.1\mathrm{V}/\AA$. (e) Transmission coefficient $T$ as a function of electron energy $E$ for different applied fields (color-coded as shown). (f) Anticrossing between the lowest-energy level in the conduction band (blue) and the highest-energy level of the valence band (red). Energy $\Delta E$ and field $\Delta \mathcal{E}$ are given with respect to the crossing point. (g) The wave functions of the anticrossing states of (f) with the corresponding color coding for $\Delta \mathcal{E}=0.14\mathrm{V}/\mathrm{cm}$. (h) The minimum splitting of the anticrossing levels as a function of the film thickness expressed as $N$. The black dots are obtained from numerical computation. The red line is calculated by using Eq. (4) and the dashed blue line from Eq. (5).

Figure 2

Electron states in metallizing fields for $N=30$. The occupied states (below Fermi energy $E_F$) are indicated by red and the vacant ones by blue. (a) Electrons in electric field $\mathcal{E}=0.144\mathrm{V}/\AA$ slightly less than the metallization threshold ${\mathcal{E}}_m=0.148\mathrm{V}/\AA$. (b) Electrons in electric field $\mathcal{E}=0.152\mathrm{V}/\AA$ slightly exceeding ${\mathcal{E}}_m$. The black double arrows denote the dominant low-frequency optical transitions. (c),(d) The same as for previous panels but for fields $\mathcal{E}=0.238\mathrm{V}/\AA$ and $\mathcal{E}=0.854\mathrm{V}/\AA$, correspondingly.

Figure 3

Optical properties of nanofilms with $N=30$ in electric fields. (a) Below metallization threshold: real (blue) and imaginary (red) parts of permittivity $\epsilon$ for fields $\mathcal{E}<{\mathcal{E}}_m$. The dashed curves correspond to the zero field, while the solid curves are for $\mathcal{E}=0.144\mathrm{V}/\AA$. (b) Above metallization threshold: $\mathrm{Re}\epsilon$ and $\mathrm{Im}\epsilon$ for $\mathcal{E}=0.152\mathrm{V}/\AA$. Two low-frequency spectral peaks correspond to the intraband transitions between the QBs. (c) The same as in the previous panel but in a stronger field $\mathcal{E}=0.238\mathrm{V}/\AA$. (d) The same as (c) but for $\mathcal{E}=0.854\mathrm{V}/\AA$. The three low-frequency absorption peaks correspond to the Franz-Keldysh effect, intraband transitions between WS states, and intraband transition between QBs, respectively, listed in the order of increasing transition frequency. (e) Combined oscillator strength of low-frequency transitions as a function of applied electric field $\mathcal{E}$. The green line is an analytical approximation—see text. (f) The real part of dielectric permittivity at zero frequency (blue) and the imaginary part (red) of the dielectric function averaged over a low-frequency spectrum ($E<3\mathrm{eV}$) as functions of the applied field. Analytical approximations (green and orange lines) are described in text.