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CAMP Seminar: Topology and correlations in two-dimensional systems
Add to Calendar 2020-01-29T20:30:00 2020-01-29T21:30:00 UTC CAMP Seminar: Topology and correlations in two-dimensional systems

Physics CAMP Seminar

Davey Laboratory (339)
Start DateWed, Jan 29, 2020
3:30 PM
to
End DateWed, Jan 29, 2020
4:30 PM
Presented By
Mathias Scheurer, Harvard University

Physics CAMP Seminar

Event Series:

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 which 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 opportunities of the 2D world using a few examples from my recent research: we will discuss an enhancement mechanism for the thermal Hall effect in the square-lattice antiferromagnet that we propose [1] to understand recent puzzling measurements in the high-temperature superconductors. Furthermore, I will review a systematic classification and energetic study [2,3] of superconductivity in twisted double-bilayer graphene, a novel moiré superlattice system. If time permits, we will also discuss an unsupervised machine learning approach that we developed [4] which is able to “learn” topological phase transitions from raw data. It will be demonstrated using the topological Kosterlitz-Thouless transition as an example, which has been found to be very difficult to capture with other, even supervised, machine-learning algorithms. 

 [1] Samajdar, Scheurer, Chatterjee, Guo, Xu, & Sachdev, Nature Physics 15, 1290 (2019).

[2] Scheurer & Samajdar, arXiv:1906.03258.

[3] Samajdar & Scheurer, to appear.

[4] Rodriguez & Scheurer, Nature Physics 15, 790 (2019).