Topological states of matter - now what?

Tami Pereg-Barnea
McGill University

Abstract

The interest in topological condensed matter dates back to the early days of the quantum Hall effect in the late 80's. Back then though, the role of topology was not entirely clear and it was thought that the interesting physics of the quantum Hall effect are unique to systems where time reversal invariance is broken. The excitement therefore grew with the discover of time-reversal invariant topological insulators in 2005.  This has led to the Nobel prize of 2016, awarded to some of the field's pioneers - Kosterlitz, Thouless and Haldane.

The introduction of topology to the classification of states of matter is arguably one of the most important paradigm shifts of our time. We now understand that states of matter should be classified not only by their dimensionality and symmetries (the notions in heard to Landau's Fermi liquid theory) but also by their topological properties.

In this talk I will present a biased view of the advances in the field and the challenges ahead. I will organize the discussion in three parts: fundamental, complex and applications. The 'fundamental' part will include research done in the direction of organizing the possible phases of materials and some known examples. The 'complex' part will focus on research into topological condensed matter systems beyond the clean, equilibrium and non-interacting limits and the 'applications' part will discuss driving, manipulating and realizing topological systems and possible applications.