Dynamic control of Casimir forces on a nanoflake in a liquid through a tunable graphene layer

The levitation of a metallic nanoflake has been experimentally demonstrated in liquid by manipulating the Casimir force with a proper choice of materials, and as a step further, dynamic control of the Casimir force acting on a nanoflake is of great importance. We show that the Casimir force acting on a nanoflake in ethanol can be dynamically controlled by adjusting the chemical potential of a graphene layer sandwiched by the Teflon film and the $\mathrm{Si}{\mathrm{O}}₂$ substrate at a distance away from the nanoflake, where the nanoflake can consist of either monolayer graphene or solid material. We develop a harmonic oscillator model that captures the dynamics of the nanoflake observed in numerical calculations. The time constant in the dynamics for a graphene nanoflake is 3 to 6 times longer than that for a gold nanoflake. The upper limit of the zero-force position of the nanoflake is discussed. Our scheme, through the use of the tunable graphene layer, significantly extends the degrees of freedom for dynamic control of nanoflakes in liquid.