Levitated spinning graphene flakes in an electric quadrupole ion trap

A method is described for levitating micron-sized few-layer graphene flakes in an electric quadrupole ion trap. Starting from a liquid suspension containing graphene, charged flakes are injected into the trap using the electrospray ionization technique and are probed optically. At micro-torr pressures, torques from circularly polarized light cause the levitated particles to rotate at frequencies $>1\text{MHz}$, which can be inferred from modulation of light scattering off the rotating flake when an electric field resonant with the rotation rate is applied. Possible applications of these techniques will be presented, both to fundamental measurements of the mechanical and electronic properties of graphene and to new approaches to graphene crystal growth, modification, and manipulation.

Figure 1

(Color) Cross section of the apex of the trap electrodes (gray regions) and the surrounding pseudopotential. The trap is made from two coaxial pieces of conically tapered stainless steel. The oscillating trap voltage is applied to the outer electrode while the inner electrode is held near ground. The surrounding vacuum enclosure (not shown) is also grounded. The tip of the inner electrode extends beyond the face of the outer electrode by about $200\mu \text{m}$.

Figure 2

Predicted velocity relaxation rate, ${\gamma }_v$, of graphene as a function of pressure.

Figure 3

Diagram showing the particle injection system and the gas handling of the experimental apparatus. The minimum obtainable pressure in the chamber is $\le 1\mu \text{torr}$.

Figure 4

Diagram of optical instrumentation for the experiments. The electric field of the light originating from the laser points out of the diagram. Light received at the detectors on average has scattered $20°$ from the incident beam direction.

Figure 5

Predicted temperature of a graphene single layer in vacuum. Solid line is versus laser power while dashed line is versus time after the heating source is turned off and the sample is cooling from a very high initial temperature. Heat is assumed to be removed from the flake by black body radiation into a surrounding environment at $T=0$, and the heat capacity is assumed to be $3k_{\text{B}}$ per C atom. The laser beam diameter is 0.5 mm, and 2.3% absorptivity and emissivity are assumed. Size effects and temperature dependence of the heat capacity have been neglected and will become increasingly important at low temperature.

Figure 6

Predicted optical signal and forward scattering cross section for graphene as a function of its size. Finite-size corrections to dipole scattering are neglected.

Figure 7

Photo of the trap with a confined visible graphene flake. The particle is on the left while scattering from the faces of the electrodes is visible on the right.

Figure 8

(Color) (a) Light scattering from a graphene flake at a pressure near the onset of the appearance of fluctuations. At higher pressure, the scattered light signal becomes uniform. (b) Behavior of a flake at low pressure. For the circular polarized light measurement, the laser is turned on at $t=0$ after being off for an extended period. Data is taken for linear polarized light after switching away from a long exposure to circular polarized light at $t=0$. The minimum signal observed using linear polarized light is limited by instrumental noise.

Figure 9

Observation of rotational resonance of a graphene flake. The light scattering off of the spinning flake measured by the photodiode is plotted as a function of time while the triangle wave modulation of the frequency of the applied electric field is superposed. Jumps in the photodiode response occur near particular frequencies of the applied field (dots), and the average value of the frequency where these jumps occur (horizontal dashed lines) is sensitive to chamber pressure. For all of the data, the sample is exposed to 4 mW circular polarized light during the measurements.

Figure 10

Effect of chamber pressure on the frequency at which rotation resonance jumps occur.

Figure 11

Spin-down behavior measured subsequent to observation of rotational resonance of the flake observed with 4 mW of linear polarized light. Previous to $t=0$, the flake had been exposed to 4 mW of circular polarized light for a long period. To facilitate the observation of the quasiperiodic oscillations, the time axis is exponentially expanded in the bottom plot.