Theory of a Two-Dimensional Rotating Wigner Cluster

A two-dimensional Wigner cluster (2DWC) with the number of electrons up to 200 in a parabolic potential well has been studied numerically and analytically. It has been shown that the inner part of the 2DWC in the axisymmetric potential well is polycrystalline, whereas electrons in outer layers form pronounced circular shells. The scaling of the cluster under the variation of the stiffness of the potential well has been considered. The threshold of the free rotation of the solid cluster in the axisymmetric potential well has been determined. The action of an alternating magnetic field generated by a coaxial solenoid on the 2DWC has been examined. It has been shown that the initially immobile solid 2DWC subjected to a weak vortex electric field begins to rotate at an angular velocity equal to half the cyclotron frequency. Furthermore, in a stronger vortex field, the cluster not only rotates but also begins to be periodically compressed, holding its structure. A further increase in the vortex field can lead to the total collapse of the cluster accompanied by the destruction of its structure. A sufficiently strong vortex electric field can also result in the differential rotation of the shells of the 2DWC. The rotational friction coefficient caused by ohmic losses in the gate, which can restrict the free rotation of the 2DWC, has been determined.