THE ROLES OF ZERO MODES IN CONDENSED MATTER PHYSICS AND HIGH-TEMPERATURE SUPERCONDUCTIVITY

Zero mode is a topological concept which plays a very fundamental role in high energy physics: Some operators can and must have zero(-eigenv alue) modes which can be used to model all observed elementary particl es, the non-vanishing masses of which are all much smaller than the Pl anck mass, and have been viewed as zero masses acquiring small masses due to spontaneous breaking of some gauge symmetries. In condensed mat ter physics zero modes can also play important roles: In the theory of soliton excitations in polyacetylene, it is the zero modes which caus e a soliton to have a reversed charge-spin relation. Recently I have f ound another interesting role played by the zero modes, this time in h igh temperature superconductivity: If high-T-c superconductors ha,ve d -wave symmetry - a proposal that is now supported by many recent exper iments, then on most surfaces and interfaces there must exist essentia lly midgap quasi-particle bound states that are essentially dispersion less. They can lead to novel properties for the system, and they most- likely have also solved a nearly-a-decade-old mystery concerning the u biquitous observations of zero-bias conductance peaks in quasi-particl e tunneling. A model study of tunneling into a multi-grained system su pports this conclusion.