Numerical study on stability of diamagnetic levitation of a single-layer graphene sheet

Strong diamagnetic interactions enable carbon materials such as graphite plates and organisms to levitate stably in the atmosphere without active control. Although the repulsive force caused by diamagnetism becomes weak as the size of the object decreases, the necessary force against gravity also decreases. Thus, a nanocarbon material such as a single-layer graphene sheet may be levitated by the diamagnetic force. However, the stability worsens as the dimensions of the sheet decrease. The dominant factors affecting the stability of the diamagnetic levitation of nanomaterials are the Brownian motion and attractive surface forces such as the Casimir interactions. We calculate the potential energy of a square graphene sheet in two states, vertical and horizontal to a magnet, and considered the transition rate between these states based on Kramers’ theory for the escape problem. Furthermore, the stiction of a single-layer graphene sheet onto a substrate caused by the Casimir force, which discontinues the levitation, is examined.