From solids with topology to black holes and back
Inclusion of topological phenomena in condensed matter physics over the past 10 years ushered a new era in this field. As a result of the groundbreaking theoretical insights entire new classes of materials with exotic properties have been discovered, including topological insulators, Dirac and Weyl semimetals as well as topological superconductors containing Majorana fermions. In this talk I will review these developments and discuss an intriguing connection noticed recently by Kitaev between one such topological system – the Sachdev-Ye-Kitaev model – and the horizon of a black hole. This connection furnishes a rare example of holographic duality between a solvable quantum-mechanical model and Einstein gravity, and may have simple physical realization in a tabletop experiment.