Topology and correlations in two-dimensional systems
Mathias Scheurer is a postdoctoral fellow working on theoretical condensed matter in Prof. Subir Sachdev's group at Harvard University.
Abstract: Two-dimensional (2D) systems have become a very active field of research due to their particularly rich physics. As we know from classical statistical mechanics, 2D systems are special as they are situated right at the lower critical dimension and, as such, just incapable of spontaneously breaking a continuous symmetry at finite temperature. Nonetheless, finite-temperature phase transitions are possible; these are, however, not characterized by a change of symmetry, but by the proliferation of topological defects, leading Kosterlitz and Thouless to introduce the concept of topological order. Furthermore, clockwise and anticlockwise exchange of particles are topologically distinct in 2D, opening the possibility of anyonic statistics, which generalizes the concept of bosons and fermions. Generally, the study of correlated electrons is particularly demanding and rich in 2D since tricks available in one dimension are not readily applicable and mean-field-based approaches are only reliable in higher dimensions. Finally, from an experimental point of view, the plethora of different heterostructures hosting 2D electron liquids and their controllability provide a rich playground for both fundamental physics and practical applications. In this talk, I will illustrate the challenges and the rich physics of the 2D world using a few examples from my recent research.