SPECIAL SEMINAR: Topology and correlations in two-dimensional systems

Two-dimensional (2D) systems have become a very active field of research due to their particularly rich physics. As we know from 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 which are not characterized by a change of symmetry, but by the proliferation of topological defects, leading Kosterlitz and Thouless (KT) 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, beyond bosons and fermions. Generally, the study of correlated electrons is particularly demanding and interesting 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 opportunities of 2D systems using examples from my recent research on unconventional superconductivity, quantum magnetism, and machine learning: I will present a comprehensive classification and energetic study [1,2] of superconductivity in twisted double-bilayer graphene, a recently realized moiré superlattice system, highlighting novel aspects of superconductivity related to the interplay of valley and spin. Furthermore, we will discuss an enhancement mechanism [3] for the thermal Hall effect in 2D antiferromagnets that is based on the proximity to a spin-liquid phase and is motivated by recent experiments on the high-temperature superconductors. If time permits, I will also present an unsupervised machine learning approach [4] which is able to “learn” topological phase transitions from raw data. It will be demonstrated using the topological KT transition as an example, which has been found to be very difficult to capture with other, even supervised, machine-learning algorithms.  

 

[1] Scheurer & Samajdar, arXiv:1906.03258.
[2] Samajdar & Scheurer, arXiv:2001.07716.
[3] Samajdar, Scheurer, Chatterjee, Guo, Xu, & Sachdev, Nature Physics 15, 1290 (2019).
[4] Rodriguez & Scheurer, Nature Physics 15, 790 (2019).