Defects with Character: Zero-Energy Majorana Modes in Condensed-Matter Systems
Abstract
Theory predicts the existence of some peculiar phases of quantum condensed matter systems, which have multiple degrees of freedom with very low energy, when localized “defects” are introduced. The speaker will focus on a class of these phases where each defect has half of a conventional degree of freedom, and the defects may be considered as sites for localized zero-energy states of a “Majorana fermion”. Such defects would also exhibit the intriguing property of “non-Abelian statistics”, that is, if various defects can be moved around each other, or if two identical defects can be interchanged, the result is 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.
In this talk, the speaker will try to explain these various concepts and discuss the attempts to realize them in condensed matter systems.
About the speaker
Prof. Bertrand Halperin received his PhD in Physics from the University of California at Berkeley in 1965. He was postdoctoral fellow at École Normale Supérieure from 1965 to 1966, and was a member of the technical staff at the Bell Laboratories after that. He joined Harvard University in 1969, and was Scientific Director of the Center for Imaging and Mesoscale Structures from 1999 to 2004. He is currently Hollis Professor of Mathematics and Natural Philosophy and Professor of Physics at Harvard.
Prof. Halperin's research interests include many aspects of the theory of condensed matter systems and statistical physics. These involve the theory of electron states and transport in small particles of a metal or semiconductor, and properties of two-dimensional electron systems at low temperatures in strong magnetic fields, or "quantum Hall systems". His current interests focus on superconductivity, transport in inhomogeneous systems, and nuclear magnetic resonance experiments in porous media. Previous research interests have included quantum antiferromagnets in one and two dimensions, low-temperature properties of glasses, melting and other phase transitions in two-dimensional systems, and the theory of dynamic phenomena near a phase transition.
Prof. Halperin received numerous awards including the Dannie Heineman Prize from the Göttingen Academy of Sciences, the Lars Onsager Prize and the Oliver E. Buckley Condensed Matter Physics Prize from the American Physical Society. In 2003, he shared the Wolf Prize in Physics with Prof Anthony J. Leggett, for their seminal contributions to the broad range of structures and processes met in condensed matter physics. He is a Member of the US National Academy of Sciences and a Fellow of the American Physical Society and of the American Academy of Arts and Sciences.
