Topological insulators and their edge states.
*** NOTE UNUSUAL DAY - FRIDAY SEMINAR***
by Victor Gurarie
Abstract: Topological insulators, or Hamiltonians with a topological band structure, are crystalline structures characterized by topological invariants. They are known to possess edge states, wave functions localized at the edge of the system whose energy fills the band gaps. They received wide prominence in condensed matter physics of the last decade with the discovery that there are many more topological insulators than was previously thought, both on theoretical and experimental level (prior to 2005, the only widely discussed topological insulator was represented by quantum particles moving in two dimensions in a magnetic field). In my talk I will show that the existence and structure of the edge states directly follows, and can be derived by simple manipulations, from the existence of the topological invariant. I will further show that the edge states are themselves topological in a certain sense and are characterized by their own topological invariant.
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