April 23, 2024, The Emergence of Topological Quantum Matter (public lecture)
Matter can arrange itself in the most ingenious ways. In addition to the solid, liquid and gas phases that are familiar in classical physics, electronic phases of matter with both useful and exotic properties are made possible by quantum mechanics. In the last century, the thorough understanding of the simplest quantum electronic phase - the electrical insulator - enabled the development of the semiconductor technology that is ubiquitous in today’s information age. In the present century, new “topological” electronic phases are being discovered that allow the seemingly impossible to occur: indivisible objects, like an electron or a quantum bit of information, can be split into two, allowing mysterious features of quantum mechanics to be harnessed for future technologies. Our understanding of topological phases builds on deep ideas in mathematics. We will try to convey that they are as beautiful as they are fundamental.
April 24, 2024, Symmetry, topology and electronic phases of matter (colloquium)
Symmetry and topology are two of the conceptual pillars that underlie our understanding of matter. While both ideas are old, over the past several years a new appreciation of their interplay has led to dramatic progress in our understanding of topological electronic materials. A paradigm that has emerged is that insulating electronic states with an energy gap fall into distinct topological classes. Interfaces between different topological phases exhibit gapless conducting states that are protected and are impossible to get rid of. In this talk we will discuss the application of this idea to the quantum Hall effect, topological insulators, topological semimetals and topological superconductors. The latter case has led to the quest for observing Majorana fermions in condensed matter, which opens the door to proposals for topological quantum computation. We will close by surveying the frontier of topological phases in the presence of strong interactions.
April 25, 2024,Topology of the Fermi Sea
The Fermi sea in a metal is a topological object characterized by an integer topological invariant called the Euler characteristic, χF. In this talk we will argue that for a 2D fermi gas χF is reflected in a quantized frequency dependent non-linear 3 terminal conductance that generalizes the Landauer conductance in D=1. We will critically address the roles of electrical contacts and Fermi liquid interactions, and we will propose experiments on 2D Dirac materials, such as graphene, using a triple point contact geometry. We will go on to show that for a D dimensional Fermi gas, χF is also reflected in the multipartite entanglement characterizing D+1 regions that meet at a point. This generalizes a well-known result that relates the bipartite entanglement entropy of a 1+1D conformal field theory to its central charge c. We will argue that for an interacting 3D Fermi liquid, χF distinguishes distinct topological Fermi liquid phases.
All talks are in SPL 59 @ 3:30pm