Joint Physics Dept - MtSE Seminar

May 23rd, Tuesday (**SPECIAL DAY**)

Topological Edge States

Prof. Emil V. Prodan

Yeshiva University

(Theoretical Condensed Matter Physics, Host: Tyson)

**SPECIAL TIME: 2:45 pm - 3:45 pm with 2:30 pm tea time

Room: ECE 202

Topological Insulators and Superconductors are fascinating states of matter displaying bulk electronic structures that cannot be deformed into the ones of ordinary insulators, without crossing a quantum phase transition. The “order parameter” of these phases is quantized and takes the form of a topological invariant that can be computed from the ground state of the system. This invariant is often, but not always, connected to a macroscopic response such as the linear and non-linear Hall or magneto-electric effects. If a boundary is cut to a topological insulator, necessarily a metallic phase appears along this boundary. This metallic phase was conjectured to remain conducting even in the presence of large disorder, hence evading the phenomenon of Anderson localization which is prevalent in 1- and 2-dimensions. In the first part of my talk, I will review all these concepts and discuss various applications which makes these materials special. In the second part of the talk, I will present specialized theoretical tools which enabled the analysis of disordered topological insulators, hence computations of realistic phase diagrams of various topological materials and a proof of their bulk-boundary correspondence principle. Recently, these tools have been used to predict new topological phases with unprecedented physical characteristics, such as a display of quantized piezo-magneto-electric effect. These new developments will be covered too.

Biography: Emil Prodan is a professor of physics at Yeshiva University. His research combines mathematics and large scale simulations to investigate the physics of complex materials. Particularly, he has pioneered the use of operator algebras, K-theory and non-commutative geometry in condensed matter theory. He is the author of two monographs, “Bulk and Boundary Invariants for Complex Topological Insulators,” and “A Computational Non-Commutative Geometry Program for Topological Insulators,” both published by Springer. His research is supported by the NSF CAREER award “Strong Disorder and Electron Interaction Effects in Topological Insulators” and by the Keck Foundation award “Engineering New Materials Based on Topological Phonon Edge Modes.” Emil received his PhD from Rice University, where he performed pioneering large scale computer simulations of optical absorption of nano-particles and, in parallel, published fundamental results on the Kohn-Sham theory. He followed with a postdoctoral position with Walter Kohn, the 1998 Nobel Laureate in Quantum Chemistry, at UC Santa Barbara. Afterwards, Emil was elected fellow of the Princeton Center for Complex Materials, where he worked Duncan Haldane, the 2016 Nobel Laureate in Physics, and Roberto Car. In 2007, Emil joined the Physics Department of Yeshiva University.