Condensed Matter Seminar

Andreev bound states in inhomogeneous superconductors

Lucian Covaci
University of British Columbia, Canada

Friday, December 1, 2006 - 4:00 P.M., NSH 184

Andreev reflections occur at the interface between a normal metal and a superconductor. An electron in the normal-metal with energy lower than the superconducting gap is reflected back as a hole while a pair enters the superconductor. In 1D systems, for such energies, the allowed states in the normal metal layer are quantized. For 2D systems the spectrum becomes continuous due to the extra degree of freedom in the direction parallel to the interface. Andreev bound states near surfaces and interfaces are investigated by obtaining numerical solutions of the Bogoliubov-de Gennes equations. We observe that Andreev states will form for superconductors with both s-wave and d-wave symmetries. Few differences appear for different surface orientations. For example, the existence of zero energy bound states at the 110 surface is only relevant to d-wave superconductivity. The study of finite size 2D superconductors has revealed localized Andreev bound states in superconducting grains surrounded by normal-metal regions. We present results for grains with different shapes and various boundary conditions.