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Mathematics Colloquium: Topological insulators and robust edge transport

Event Type
Lecture
Sponsor
Department of Mathematics
Location
Altgeld 245
Date
Dec 5, 2024   4:00 pm  
Speaker
Guillaume Bal (Chicago)
Views
53
Originating Calendar
Mathematics Colloquium & Named Lectures

Abstract:

Surprising asymmetric transport phenomena along interfaces separating insulating bulks have been observed in many areas of applied sciences, e.g., electronics, photonics, and geophysics. Such transport displays strong robustness to perturbations as an obstruction to Anderson localization. In fact, it affords a topological origin: systems in the same topological class display similar robust, quantized, interface transport.

This talk considers systems modeled by elliptic partial differential operators on the Euclidean plane. We introduce a simple topological classification by means of confining domain walls, which provides an explicit computation of a topological invariant, technically the index of a Fredholm operator. We next define a physical observable that allows us to quantify the asymmetry of the edge transport. The evaluation of such an observable is challenging in practice. We finally present a bulk-edge correspondence, a pillar of topological phases of matter in the physical literature, stating that the interface current observable is in fact equal to the aforementioned simple topological invariant.

The theoretical findings are illustrated with examples ranging from electronics applications to geophysical fluid flows.

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