"Topological Matter and Why You Should Be Interested"
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In two dimensional topological phases of matter, processes depend on gross
topology rather than detailed geometry. Thinking in 2+1 dimensions, particle
world lines can be interpreted as knots or links, and the amplitude for certain
processes becomes a topological invariant of that link. While sounding rather
exotic, we believe that such phases of matter not only exist, but have actually
been observed in quantum Hall experiments, and could provide a uniquely
practical route to building a quantum computer. Possibilities have also been
proposed for creating similar physics in systems ranging from superfluid helium
to strontium ruthenate to semiconductor-superconductor junctions to quantum
wires to spin systems to cold atoms.