The study of 2D materials is a rapidly growing area of research, where the ability to isolate and probe an individual single-layer specimen is of high importance. The levitation approach serves as a natural solution for this problem and can be used in ways complementary to the standard techniques. Experiments, including study of properties at high or close to melting temperatures, stretching, folding, vibration and functionalization, can be conducted on levitated 2D materials. As a first step towards realization of all these ideas, one needs to develop and test a system allowing for control over the thermal state and orientation of mono-layer flakes.

In this thesis, I present the results of implementation of the parametric feedback cooling scheme in a quadrupole ion trap for stabilization and cooling of graphene nanopletelets. I have tested and showed that the feedback allows to stabilize levitated graphene nanoplatelets in high vacuum conditions (<1 microTorr) to have trapped life times longer than a week. Cooling of the center of mass motion to temperatures below 20 K for all translational degrees of freedom was observed.

I have also studied the coupling of DC patch potentials, which were found to be present in the high vacuum chamber. Their effect on cooling was studied and the protocol for minimizing the noise coupling created by the DC fields was designed. We have shown that by varying DC voltages on a set of auxiliary DC electrodes, placed near the trap, one can balance out the DC fields and achieve the lowest cooling temperature. The settings corresponding to this temperature were measured to have a slow drift in time. Ability to tune the settings to balance this drift without breaking the vacuum was studied and found to be a viable solution for the drift cancellation.

In addition, our effort in characterization of the flakes is presented. It was shown that the flake discharge quantization observed during the initial pumping down of the high vacuum chamber allows to extract absolute values of flake mass and charge. I also mention the issues experienced with estimation of the shape of the flake, as well as its temperature based on an equipartition theorem.

Finally, I discuss the preliminary data on the precession and reorientation of the flakes in the presence of circularly polarized light (CPL) and DC stray fields. The dependence of flake orientation on the offset from the nulling settings is observed and is explained in terms of basic model of a solid charged disk in the presence of two torques created by CPL and DC stray fields.