Topological Boundary Modes from Quantum Electronics to Classical Mechanics

The 2015 Cherwell-Simon Lecture delivered by Professor Charles Kane Over the past several years, our understanding of topological electronic phases of matter has advanced dramatically. A paradigm that has emerged is that insulating electronic states with an energy gap fall into distinct topological classes. Interfaces between different topological phases exhibit gapless conducting states that are protected topologically and are impossible to get rid of. In this talk we will discuss the application of this idea to the quantum Hall effect, topological insulators, topological superconductors and the quest for Majorana fermions in condensed matter. We will then show that similar ideas arise in a completely different class of problems. Isostatic lattices are arrays of masses and springs that are at the verge of mechanical instability. They play an important role in our understanding of granular matter, glasses and other ‘soft’ systems. Depending on their geometry, they can exhibit zero-frequency ‘floppy’ modes localized on their boundaries that are insensitive to local perturbations. The mathematical relation between this classical system and quantum electronic systems reveals an unexpected connection between theories of hard and soft matter.

Om Podcasten

The Department of Physics public lecture series. An exciting series of lectures about the research at Oxford Physics take place throughout the academic year. Looking at topics diverse as the creation of the universe to the science of climate change. Features episodes previously published as: (1) 'Oxford Physics Alumni': "Informal interviews with physics alumni at events, lectures and other alumni related activities." (2) 'Physics and Philosophy: Arguments, Experiments and a Few Things in Between': "A series which explores some of the links between physics and philosophy, two of the most fundamental ways with which we try to answer our questions about the world around us. A number of the most pertinent topics which bridge the disciplines are discussed - the nature of space and time, the unpredictable results of quantum mechanics and their surprising consequences and perhaps most fundamentally, the nature of the mind and how far science can go towards explaining and understanding it. Featuring interviews with Dr. Christopher Palmer, Prof. Frank Arntzenius, Prof. Vlatko Vedral, Dr. David Wallace and Prof. Roger Penrose."