Condensed Matter Physics: The Rise of Topology.
One of the astonishing things in physics is that abstract mathematical concepts often find meaning in physical phenomena. Maxwell, Einstein, Heisenberg: each developed theories of nature which depend in part on mathematical machinery that preceded them. Today as part of a “rise of topology”, condensed matter physics is going through a mini-revolution, with its origins in mathematical concepts of Carl Gauss.
What has been discovered, is that when matter is topological, hidden twists in
the order parameter or in the wavefunction manifest themselves as wonderful new
properties. For instance, superconductors conduct current because of the
topological stability of twists in the phase. But more recently, we’ve
found that when an insulator is topological, it becomes metallic on its
surface, with weird neutrino-like surface excitations which are spin polarized
along their direction of motion. A few years ago, a group of physicists at
Rutgers and Maryland Universities were led to predict that a novel insulator,
SmB6, discovered 40 years ago in New Jersey, is topological. I’ll tell you
about the flurry of experiments across the globe which have tentatively
confirmed this prediction, but also why its still a big controversy.
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