Conductance of molecularly linked gold nanoparticle films across an insulator-to-metal transition: From hopping to strong Coulomb electron-electron interactions and correlations

We study the influence of Coulomb effects on conductance $\left(g\right)$ of 1,4-butanedithiol-linked gold nanoparticle (NP) films near a percolation insulator-to-metal transition. On the insulating side, $g\sim \exp [-{(T_{\circ }/T)}^{1/2}]$, where $T$ is absolute temperature, a behavior predicted by Efros-Shklovskii's theory for charges optimizing pathways that accommodate Coulomb charging barriers. On the metallic side below $\sim 20$ K, $g$ varies linearly with $T^{1/2}$. Such a correction to $g(T=0)$ is predicted by Altshuler-Aronov's theory for Fermi liquid metals when disorder mediates electron-electron $\left(e\text{−}e\right)$ Coulomb interactions. Remarkably, in the present system, the $T^{1/2}$ component of $g$ is significant compared to $g(T=0)$, and fitting to Boltzmann's transport theory yields elastic scattering lengths that are anomalously small—much smaller than the distance between atoms (Ioffe-Regel limit required for metals). Previous studies of materials such as fullerites, layered organic salts, and transition metal compounds have also reported such anomalously small scattering lengths and large $T^{1/2}$ components and attributed them to strong Coulomb mediated $e\text{−}e$ correlations, which we believe is likely the case in the present system as well. This study highlights a potential opportunity to use molecularly linked nanoparticle films as a platform to study strongly correlated electrons in a controlled fashion.

Figure 1

(a) A schematic showing fabrication of molecularly linked gold nanoparticle films. (b) Transmission electron microscope image of gold nanoparticles. (c) Absorbance (610 nm) vs number of gold nanoparticle + butanedithiol immersion cycles. (d) Scanning electron microscope images of gold nanoparticle films self-assembled on a silicon substrate with one to four immersion cycles (left to right).

Figure 2

Conductance $\left(g\right)$ vs temperature $\left(T\right)$ for various butanedithiol-linked hold nanoparticle films with various numbers of dithiol/nanoparticle immersion cycles. Conductance is normalized to $g$(300 K). Values of $g$(300 K) range from 0.0155 to $7.63\times {10}^{-6}{\Omega }^{-1}$. (Inset) Magnification of the data shown in the main panel at low temperatures. The data have been normalized to $g$(20 K). Values of $g$(20 K) range from 0.0164 to $1.35\times {10}^{-6}{\Omega }^{-1}$.

Figure 3

Arrhenius plots of conductance for various butanedithiol-linked gold nanoparticle films near the insulator-to-metal transition. The films have $\text{log}\left(r_{2\mathrm{K}}\right)$ values that range from 3.79 to 6.10.

Figure 4

(a) $\text{ln}[g/g(20\text{K}\left)\right]$ vs $T^{-1/2}$ and (b) $g/g$(20 K) vs $T^{1/2}$ for various molecularly linked gold nanoparticle films. $\text{log}\left(r_{2\mathrm{K}}\right)$ values of the films range from 3.79 to 4.21 (group i) and 4.37 to 6.10 (group ii). Plots for the two groups of data sets are offset for clarity.

Figure 5

A comparison of the goodness of fits using $g/g$(20 K) vs $T^{1/2}$ and $\ln [g/g$(20 K)] vs $T^{-1/2}$ models for various films near the insulator-to-metal transition.