Tunable Casimir equilibria with phase change materials: From quantum trapping to its release

A stable suspension of nanoscale particles due to the Casimir force is of great interest for many applications such as sensing, noncontract nanomachines. However, the suspension properties are difficult to change once the devices are fabricated. Vanadium dioxide (${\mathrm{VO}}_2$) is a phase change material, which undergoes a transition from a low-temperature insulating phase to a high-temperature metallic phase around a temperature of 340 K. In this work, we study Casimir forces between a nanoplate (gold or Teflon) and a layered structure containing a ${\mathrm{VO}}_2$ film. It is found that stable Casimir suspensions of nanoplates can be realized in a liquid environment, and the equilibrium distances are determined, not only by the layer thicknesses but also by the matter phases of ${\mathrm{VO}}_2$. Under proper designs, a switch from quantum trapping of the gold nanoplate (“on” state) to its release (“off” state) as a result of the metal-to-insulator transition of ${VO}_2$, is revealed. On the other hand, the quantum trapping and release of a Teflon nanoplate is found under the insulator-to-metal transition of ${\mathrm{VO}}_2$ . Our findings offer the possibility of designing switchable devices for applications in micro and nanoelectromechanical systems.

Figure 1

(a) Schematic view of a gold nanoplate suspended in a liquid environment. (b) The permittivity of different materials (gold, ${\mathrm{VO}}_2$, bromobenzene, and Teflon) as a function of imaginary frequency.

Figure 2

Casimir pressure via different thicknesses of ${\mathrm{VO}}_2$, where the thickness $L_{\mathrm{T}}=45$ nm and $L_g=40$ nm are fixed. (a) Thick films. The solid and dashed lines represent the pressure for the metallic and insulating phases of ${\mathrm{VO}}_2$, respectively. (b) Thin films. The positive (negative) sign of the pressure corresponds to the repulsive (attractive) force.

Figure 3

Casimir pressure contributed from different frequencies and different parallel wave vectors. (a) and (b) $d=30$ nm; (c) and (d) $d=85$ nm (close to critical separation); (e) and (f) $d=150$ nm. (a), (c), and (e) ${\mathrm{VO}}_2$ in the metallic phase ($T>T_c$); (b), (d), and (f) ${\mathrm{VO}}_2$ in the insulating phase ($T<T_c$). The layer thicknesses are set as $L_{\mathrm{V}}=20$ nm and $L_{\mathrm{T}}=45$ nm.

Figure 4

(a) The equilibrium distances via the thicknesses of ${\mathrm{VO}}_2$ under three different configurations (see the inset on the right). The thickness $L_{\mathrm{T}}$ is set as 45 nm. The solid (dashed) curves for type III represent stable (unstable) equilibria. Contour plots of Casimir pressure via the thicknesses of coating Teflon for (b) metallic ${\mathrm{VO}}_2$ and (c) insulating ${\mathrm{VO}}_2$, where the thickness $L_{\mathrm{V}}=20$ nm is fixed. In (b) and (c), the gray zones represent a strong repulsive pressure larger than 1 Pa. The colors of the curves denote the same meaning as those in (a).

Figure 5

Casimir pressure for a complementary design. A thin film of ${\mathrm{VO}}_2$ with thickness $L_{\mathrm{V}}$ is deposited on a Teflon substrate. (a) The metallic ${\mathrm{VO}}_2$; (b) The insulating ${\mathrm{VO}}_2$. The thickness of the suspended nanoplate is set as 100 nm.

Figure 6

Casimir pressure calculated for finite temperatures and 0 K approximation from Eq. (1). (a) The trapping and release of a gold nanoplate. The parameters for the substrate are $L_{\mathrm{T}}=45$ nm and $L_{\mathrm{V}}=20$ nm. (b) The trapping and release of a Teflon nanoplate. The thickness $L_{\mathrm{V}}$ is set as 2 nm.

Figure 7

The total energy of (a) a suspended gold nanoplate and (b) a Teflon nanoplate under different types of gravity projection. The solid and dashed lines represent the cases for the metallic ${\mathrm{VO}}_2(T=360$ K) and insulating ${\mathrm{VO}}_2(T=320$ K), respectively. The in-plane area A is set as $10\mu \text{m}\times 10\mu \text{m}$. Other parameters are kept the same as those in Fig. 6.