Topology in Condensed Matter, from Vortices to Symmetry Protected Topological Phases: The Influential Works of the 2016 Nobel Laureates
| Date/Time: | Monday, 05 Dec 2016 from 4:10 pm to 4:10 pm |
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| Location: | Phys 0003 |
| Phone: | 515-294-5441 |
| Channel: | College of Liberal Arts and Sciences |
| Actions: | Download iCal/vCal | Email Reminder |
Abstract
The 2016 Nobel Prize in Physics was awarded to David J. Thouless, F. Duncan M. Haldane and J. Michael Kosterlitz for "theoretical discoveries of topological phase transitions and topological phases of matter." In this colloquium, we will explore the important role that topology plays in condensed matter physics.
Most phases of matter can be understood by the symmetries that they break: crystalline phases break translation symmmetry, nematic order breaks rotation symmetry and ferromagnetism breaks time-reversal symmetry. While symmetry breaking is a macroscopic phenomenon, it can be understood and measured locally. Moreover, strong thermal and quantum fluctuations can destroy symmetry breaking order in sufficiently low dimensions. Over the last thirty years, it has become clear that symmetry breaking alone cannot describe all phases of matter. Kosterlitz and Thouless were first to show that, while symmetry breaking is forbidden by the Hohenberg-Mermin-Wagner theorem, two-dimensional systems such as thin superfluid films or 2D planar magnets undergo a finite temperature phase transitions that is associated with an unbinding of topological (vortex) excitations.
Another hallmark of topological phases is the quantization of physical phenomena such as the transverse Hall conductivity, which is pinned at integer values in the integer quantum Hall effect (QHE) or at certain fractional values in the fractional QHE. The work of D. M. Haldane, e.g. on the integer QHE without external magnetic field, underlies the recent boom on symmetry-protected topological phases of matter, which includes topological insulators and superconductors. The electronic wavefunctions in these phases are characterized by non-zero topological invariants that give rise to an intriguing correspondence between insulating bulk and symmetry-protected topological metallic surface states.