Charge-Induced Fluctuation Forces in Graphitic Nanostructures

Charge fluctuations in nanocircuits with capacitor components are shown to give rise to a novel type of long-ranged interaction, which coexist with the regular Casimir–van der Waals force. The developed theory distinguishes between thermal and quantum mechanical effects, and it is applied to capacitors involving graphene nanostructures. The charge fluctuations mechanism is captured via the capacitance of the system with geometrical and quantum mechanical components. The dependence on the distance separation, temperature, size, and response properties of the system shows that this type of force can have a comparable and even dominant effect to the Casimir interaction. Our results strongly indicate that fluctuation-induced interactions due to various thermodynamic quantities can have important thermal and quantum mechanical contributions at the microscale and the nanoscale.

Popular Summary

Electromagnetic fluctuation-induced interactions, such as Casimir and van der Waals forces due to dipolar fluctuations, are ubiquitous in nature. These interactions are particularly prominent at microscales and nanoscales, and they are critically important for the stability of various types of composites. Similar to dipolar fluctuations, ionic charge-density fluctuations, which determine the behavior of ionic solutions, can mediate an attractive dispersive force between bounding surfaces. We show that a new fluctuation mechanism hinging on monopolar charge fluctuations of objects can be quite important, and it can result in a dispersive interaction similar to Casimir and van der Waals forces.

We consider a parallel-plate capacitor made of a graphene nanostructure and a metallic substrate. Charge fluctuations, transferred on the capacitor by a connecting wire, induce a dispersive attractive force between the plates, which becomes especially prominent in nanostructures. Our novel theory utilizes the quantum capacitance concept, and it distinguishes between thermal and quantum mechanical contributions. We demonstrate that the charge-induced fluctuation force exists in conjunction with the more commonly studied Casimir force and that it can even become stronger than the Casimir force.

Our results are strong evidence that there are different types of dispersive interactions, which can enable additional studies of the properties of materials at the microscale and nanoscale.

Figure 1

(a) Ideal system under consideration. A parallel plate capacitor connected by a wire supporting voltage fluctuations $\delta V$. One of the plates can be a graphene ribbon with a width $w$ above a thick metallic substrate separated by a distance $z$. The capacitor system is assumed to be in an environment of air with $\epsilon \approx 1$. (b) Experimentally realistic setting. The wire is represented by a metallic connection between the “bottom” metal plate and the “top” graphene nanoribbon.

Figure 2

(a) $C_Q$ as a function of chemical potential for graphene and a GNR with $w=12.4\mathrm{nm}$. (b) Charge fluctuations thermal force normalized by ${\overline{f}}_0=-k_{B}T/(2Az)$. The area of all ribbon structures is $1\mu {\mathrm{m}}^2$ and $\mu =0.1\mathrm{eV}$. The graphene-metal Casimir force normalized by ${\overline{f}}_0$ at room temperature is also shown. The metal plasmon energy is taken as $\hslash {\omega }_p=9\mathrm{eV}$. (c) The normalized charge fluctuations thermal force versus chemical potential for different GNRs at $T=300\mathrm{K}$.

Figure 3

(a) Charge fluctuations force versus distance between ribbon of width $0.1\mu \mathrm{m}$ and area $1\mu {\mathrm{m}}^2$ and a metal plate at room temperature, where $C^t(\omega )$ is used. Typical values for $\tau$ and $R$ are taken. (b) The normalized by ${\overline{f}}_0$ charge fluctuations force as a function of the wire resistance for different relaxation times.