Lise Meitner Distinguished Lecture: Defects with Character: Zero-Energy Majorana Modes in Condensed-Matter Systems

Theory predicts the existence of some peculiar phases of quantum condensed matter systems, in which there are extra degrees of freedom with very low energy, if localized “defects” are present. In one class of these phases, the size of the low-energy Hilbert space corresponds to one-half degree of freedom per defect, and the defects are said too be sites of localized zero-energy “Majorana modes”. The defects are predicted to obey “non-Abelian statistics” — i.e., if various defects can be moved around each other, or if two identical defects can be interchanged, the result will be a unitary transformation on the quantum mechanical state that depends on the order in which operations are performed, but is insensitive to many other details. The talk will introduce these concepts and discuss some attempts to realize them in condensed matter systems.