Seminar Notice

Speaker Dr. Jun Won Rhim (Max Planck Institute for the Physics of Complex Systems)
Date & Time 2017.07.18, 00:00~00:00
Place Bldg. 19, Rm. 210
Title Unified bulk-boundary correspondence for band insulators
Contents

The bulk-boundary correspondence(BBC), being a longstanding question in the solid state physics, is the most quintessential idea in the topological classification of matter. However, the BBC has never been proved in general, and even there exist counterexamples in the Berry phase's BBC of 1D reflection symmetric insulators. In 1D, we develop two general bulk numbers for the exact and even-odd predictions of the number of in-gap modes. In higher dimensions, we find a novel winding number, so called the pole winding number, that describes the number and topological characters of robust metallic surface bands in the gap. This is done by connecting bulk and boundary continuously, and observing evolutions of poles of the Green's function during that process in the vicinity of bulk band edges. All the numbers can be applied to general insulating phases in a unified manner regardless of their underlying symmetries, and evaluated effectively without any gauge fixing problems. Using those numbers, we successfully apply our BBC to various systems including above-mentioned counterexamples in 1D, predict the existence of boundary modes on various kinds of graphene's edges such as open boundaries and grain boundaries, and revisit the Kane-Mele model and topological insulators.

 

Hos t : Prof. Bohm Jung Yang