Boundary Layers in Superconductors and Liquid Crystals

Louisiana State University, Baton Rouge LA

Investigators

Abstract

Almog DMS-0604467 The project covers both the Ginzburg-Landau model of superconductivity and the Landau-De Gennes model of liquid crystals. The investigator studies several fundamental theoretical problems related to these models. In particular, he examines: 1. The structure of boundary layers of superconducting or smectic states that are both characterized by exponentially fast decaying solutions. For the case of superconductors this phenomenon is called surface superconductivity. 2. The emergence of periodic solutions, known as Abrikosov lattices for superconductors and as twist grain boundaries for smectic liquid crystals. 3. The loss of stability, in the presence of a combination of electric and magnetic field, of the normal state in superconductors. Superconductors are metals that when put under a sufficiently low temperature exhibit two important properties: 1. They lose entirely their electrical resistivity. 2. The magnetic field is excluded from the superconducting area. Superconductors have enormous technological potential for applications ranging from magnetic sensors, through generators of large magnetic fields, to high power transmitters. Liquid crystals contain elongated molecules whose direction and density determine the material's mechanical, optical and other properties. They are already at the heart of a large industry, particularly in display devices, and they are being explored for further application in a variety of optical devices. Liquid crystals with uniform density are called nematics, and those with non-uniform density are termed smectics. The investigator studies the behavior of the above materials when the material is either superconducting or smectic only in a thin layer near the boundary. The project could shed light on the transition from the normal state to the superconducting one, or from nematics to smectics. It can also have some industrial applications because it aims at finding the maximal current a superconductor can carry before reverting to the normal state where the material resistivity would cause energy losses.