| Details: |
We will provide an introduction to topological systems in physics.
Several examples of these are now known: these include quantum Hall
systems, topological insulators in two and three dimensions, and p-wave
superconducting wires. In all of them, the bulk states are gapped and
therefore insulating, while the boundaries have gapless states which can
lead to electron transport at low temperatures. The number of boundary
states is given by a topological invariant, such as winding number or
Chern number. The boundary states have many interesting properties.
For instance, the states on the surface (edge) of a three-dimensional
(two-dimensional) topological insulator satisfy the Dirac equation with
spin-momentum locking, while the states at the ends of a p-wave
superconductor wire are Majorana fermions.
Two new kinds of topological systems have been studied recently:
some two-dimensional spin systems have magnon bands which have a Chern
number and show a thermal Hall effect, and Josephson junctions of three
or more superconducting wires have Andreev bound states whose bands have
a Chern number which can be detected through the AC Josephson effect.
We will present an overview of a number of these systems. |