Negative vacuum friction in terahertz gain systems

Two objects in relative motion without physical contact suffer a friction force, resulting from vacuum fluctuation. It is widely accepted that friction acts in the opposite direction of the relative velocity. Here, this study demonstrates the existence of negative friction, where the direction of friction is along the sliding direction, in a gain system. The system consists of a vacuum-separated silica sphere and a dielectric substrate covered by a graphene sheet (gain medium). The friction torque of the rotating sphere can be switched between positive and negative, depending on the quasi-Fermi energy of graphene. Negative vacuum friction can be achieved when the quasi-Fermi energy is large, and its magnitude is strongly dependent on the distance, temperature, and permittivity of the substrate. For moderate conditions, the torque generated by negative friction surpasses the resistance posed by the surrounding air, presenting a different approach for driving nanoparticles to an ultrahigh rotating speed.

Figure 1

(a) Schematic view of the system under study. A silica nanosphere with rotational frequency $\mathrm{\Omega }$ is suspended in the vacuum. The dielectric substrate with permittivity ${\epsilon }_{\mathrm{sub}}$ is covered by a graphene sheet, which can be a gain medium by applying an external pump light or electrical bias. (b) Contour plot of the real part of graphene conductivity, normalized by ${\sigma }_0=e^2/\hslash$. The nanosphere and the substrate is in room temperature with $T_1=T_2=300$ K.

Figure 2

(a) $\text{Im}\left[G\right(\omega \left)\right]$ for a dielectric substrate ${\epsilon }_{\mathrm{sub}}=2$ covered by an active graphene sheet; (b) and (c) represent $\text{Im}\left[G\right(\omega \left)\right]$ contributed by different wave vectors with ${\mu }_F=10$ meV and ${\mu }_F=50$ meV, respectively. The green dashed lines in (b) and (c) represent the dispersion of SPPs for the TM mode.

Figure 3

(a) Friction torque vs quasi-Fermi energy of graphene under different separations, where the temperature $T=300$ K is fixed. (b) Friction torque vs quasi-Fermi energy of graphene under different temperatures, where the separation $d=300$ nm is fixed. We set the rotational frequency $\mathrm{\Omega }/2\pi =5$ GHz and ${\epsilon }_{\mathrm{sub}}=2$.

Figure 4

Friction torque vs quasi-Fermi energy of graphene under different substrates for (a) $\mathrm{\Omega }/2\pi =5$ GHz and (b) $\mathrm{\Omega }/2\pi =5$ THz. Here, we set $d=300$ nm, $T=300$ K.

Figure 5

$\text{Im}\left[G\right(\omega \left)\right]$ for a graphene-covered substrate of (a) ${\mathrm{SiO}}_2$ and (b) SiC. The arrows indicate the resonant exciations of the SPPs in graphene and SPhPs in the polar substrates. The dashed lines represent the gain/loss boundary of graphene.

Figure 6

(a) The friction torque vs the rotational frequency from the microwave to sub-THz regime. The minus sign in the legend represents the negative friction. (b) The contrast of friction torque and air resistance at the THz regime. ${\mu }_F=100$ meV.