Multielectron bubbles in helium as a paradigm for studying electrons on surfaces with curvature

The study of two-dimensional electronic systems has revealed a host of new and startling phenomena, such as the quantum Hall effect. Although effort has gone into studying the effects of confinement in two-dimensional systems, the effects of surface curvature remain relatively unexplored. Nevertheless, curvature and surface topology are expected to have a profound influence: for example, on a sphere it is not possible to have a non-trivial current field that has no vortex structure in it. The spherical geometry also influences lattices in that topological lattice defects are always present. In this report, we present results and recent insights into the physics of electrons on spherical surfaces. In particular, we investigate the case of multielectron bubbles. Multielectron bubbles are (micron sized) cavities inside liquid helium, containing electrons that collect in a nanometer thin film on the surface of the bubble and form a spherical two-dimensional electronic system. Different phases are identified and investigated: the electron fluid, the Wigner lattice, and the pair-correlated “superconducting” state. Uniaxial external magnetic fields (normal to the surface at the poles of the sphere, and tangential to the surface at the equator) influence the different phases and give rise to textures on the surface. In discussing the properties of the spherical electron system under various conditions, we identify the differences between flat surfaces and spherical surfaces. The theoretical framework presented here is focused on the case of electrons on the spherical surface of a bubble in helium. We discuss how the theory can straightforwardly be generalized to investigate the case of (finite thickness) metallic nanoshells. Nanoshells consist of a non-conducting nanograin covered by a few atomic layers of metal. The physiologically compatible size and unique optical properties of these objects have led to applications in diagnostics and directed therapeutics of cancer and drug delivery. These successful biomedical applications underline the increasing interest in curved-surface electron systems treated in this report, and the necessity to supply a theoretical framework for these systems. Multielectron bubbles and nanoshells are structures that are realizable in nature. We begin this report by discussing the experimental developments and progress in producing these entities in a useful manner that allows them to be studied and utilized.