Dynamic and fluctuation properties of a graphene disk levitated by a diamagnetic force in air

Abstract

A graphene disk can be levitated above a magnet by a repulsive force arising from their diamagnetic interaction if the product of the magnetic field and its gradient is sufficiently large. The diamagnetic force also causes the rotation of the graphene disk because of the strong anisotropy of the magnetic permeability of graphene; thus a motion of centroid and rotation are considered by solving simultaneous Langevin equations. Furthermore, the dependence of a fluctuations of the position and angle of the levitated graphene disk on the size and temperature is also explained.

Stabilizing Diamagnetic Levitation of a Graphene Flake through the Casimir Effect

“…However, the Casimir energy diverges to negative infinity. This implies that the levitation state is metastable [35][36][37], and a potential barrier is present near the surface. The height of this potential barrier is not significant.…”

Continuous limit of a tight-binding model on a hexagonal disk in a magnetic field: size dependence on energy level

“…Magnetic properties of a graphene sheet originate from its orbital electric current and spin characteristics. The strong diamagnetism of graphene arises from the former characteristic [7,8], which generates enough repulsive force to levitate a micrometer-size multi-layer graphene disk above a magnet [9,10]. To consider the diamagnetic properties in a mesoscopic scale, a calculation method other than the exact diagonalization applied in tight-binding models is required.…”